Evaluating All Six Trigonometric Functions
Finding the values of all six trigonometric functions of an angle given a right triangle
Problem: Solve the following equation:\[
\tan{(x)} + 4 = 5\tan{(x)}, \quad 0 \leq x < 2\pi
\]
Finding the values of all six trigonometric functions of an angle given a right triangle
Evaluating the other five trigonometric functions for an acute angle given the value of sine
Evaluating the other five trigonometric functions given sine and that tangent is negative
Solving a trigonometric equation with sine and cosine on a given interval
Solving an quadratic-like equation with sine by factoring
Solving an equation with cosine on a given interval
Solving a trigonometric equation with sine on a given interval
Evaluating compositions with inverse trigonometric functions
Writing an equivalent algebraic expression for compositions with inverse trigonometric functions containing variables
Using inverse trigonometry to write an expression for an angle in a right triangle
Verifying a trigonometric identity
Solving a trigonometric equation
Solving a trigonometric equation
Using a double angle formula to solve a trigonometric equation
Using a double angle formula to solve a trigonometric equation
Using a difference formula to evaluate a trigonometric function
Using a sum formula to evaluate a trigonometric expression
Using a sum formula to evaluate a trigonometric expression
Finding the properties of a transformed tangent function and graphing it
Review of limits and derivatives of inverse trigonometric functions
Review of limits and derivatives of inverse trigonometric functions
Properties and derivatives of inverse trigonometric functions
Properties and derivatives of inverse trigonometric functions
Simplifying expressions containing trigonometric and inverse trigonometric functions
Evaluating compositions of trigonometric and inverse trigonometric functions
Calculating a composition of tangent and arcsine
Review of trigonometric substitution
Using trigonometric identities to integrate powers of secant and tangent
Review of limits and derivatives of inverse trigonometric functions
Properties of inverse trig functions and the derivative of arctangent
Properties and derivatives of inverse trigonometric functions
Proving the derivatives of trigonometric functions and that sine is continuous
Properties and derivatives of inverse trigonometric functions
Review of trigonometric substitution
Using trigonometric identities to integrate powers of secant and tangent
Integrating using a trigonometric substitution
Explaining the trigonometric ratios of right triangles for sine, cosine, and tangent
Using trig to find the length of the side of a right triangle given an angle and side length
Finding the exact value of tangent for several given angles using the unit circle
Using the unit circle to sketch the graph of the tangent function
Graphing the reciprocal trig functions cosecant, secant, and cotangent
Using the Half-Angle Identities to find the exact values of sine, cosine, and tangent
Solving a trigonometric equation with tangent and sine by factoring
Solving a trig equation with sine and tangent using a trig identity
Evaluating all six trigonometric functions for angles in degrees and radians
Evaluating all six trigonometric functions for a right triangle
Evaluating all six trigonometric functions for a right triangle
Using trigonometry to determine the height of a tree
Evaluating trigonometric functions given a point on the terminal side of an angle
Evaluating trigonometric functions given a point on the terminal side of an angle
Finding trigonometric functions given information about the angle
Evaluating a composition of tangent and arccosine
Sketching one period of a transformed sine graph
Finding the amplitude, period, phase shift, and vertical shift for a given sine function
Writing a cosine function for a given graph
Review of limits and derivatives of inverse trigonometric functions
Solving a limit example with a trigonometric functions
Solving a limit example with a trigonometric function
Evaluating a trigonometric limit using trigonometric identities
Determining the properties of a sine function and graphing it
Writing the equation for a sine function with certain characteristics
Determining the properties of a cosine function and graphing it
Writing the equation for a cossine function with certain characteristics
Writing the equation for a sine function to match a given graph
Writing the equation for a cosine function to match a given graph
Evaluating a composition of trigonometric and inverse trigonometric functions
Evaluating compositions with inverse trigonometric functions
Verifying a trigonometric identity
Solving a trigonometric equation
Solving a trigonometric equation by factoring
Solving a trigonometric equation
Solving a trigonometric equation
Solving a trigonometric equation
Using a double angle formula to solve a trigonometric equation
Using double angle formulas to evaluate trigonometric functions
Using a sum formula to rewrite a trigonometric expression
Using the Law of Sines to solve a triangle
Using the Law of Sines to solve a triangle
Using the Law of Cosines to solve a triangle
Using the Law of Sines to solve a triangle
Derivatives and vectors with some physics applications
Review of the limit definition of a derivative and calculating the derivative
Derivatives of exponential functions and the exponential model
Reviewing the chain rule and the derivatives and limits of trigonometric functions
Review of the limit definition of a derivative and calculating the derivative
Review of derivatives and tangent lines to functions and vector equations
Approximation and Newton's Method, and limits and derivatives of exponential functions
Limits at infinity and asymptotes, along with physics applications
Limits at infinity, asymptotes, and tangent lines
Review of the limit definition of a derivative and calculating the derivative
Review of derivatives and tangent lines to functions and vector equations
Differentials, linear approximations and quadratic approximations
Review of the limit definition of a derivative and calculating the derivative
Derivatives and tangents to curves
Derivatives of trigonometric functions and using the Chain Rule
Approximation and Newton's Method, and limits and derivatives of exponential functions
Derivatives of trigonometric functions and using the Chain Rule
Derivatives and vectors with some physics applications
Derivatives of exponential and logarithmic functions and the exponential model
Derivatives and vectors with some physics applications
Derivatives of exponential and logarithmic functions and the exponential model
Using derivatives to find properties of graphs
Using derivatives to find properties of graphs
Using L'Hospital's Rule to solve limits
Evaluating a composition of trigonometric and inverse trigonometric functions
Finding a Cartesian equation for a parametric curve
Using vectors to find the magnitude and direction of a resultant force
Using the Chain Rule to differentiate functions with exponential and trigonometric functions
Using the Chain Rule to differentiate a function containing trigonometric functions
Using the Product, Quotient and Chain Rules to find several derivatives
Using the Quotient and Chain Rules to find several derivatives
Finding the derivative of an implicit function
Finding the derivative of an implicit function
Finding the antiderivative of a function with secant and tangent
Converting parametric equations into a Cartesian equation
Converting parametric equations into a Cartesian equation and graphing
Converting parametric equations into a Cartesian equation and graphing
Evaluating an integral using integration by parts
Evaluating an integral using trigonometric identities
Evaluating an integral using trigonometric identities
Using trigonometric identities to integrate powers of sine and cosine
Using a trigonometric identity to integrate powers of secant and tangent
Using a trigonometric identity to integrate powers of secant and tangent
Using trigonometric identities to integrate powers of cosine and tangent
Integrating a function with sine using u-substitution
Explaining the cases for using trigonometric substitution
Proving facts about the derivatives of vector functions including the product rule
Derivatives and vectors with some physics applications
Derivatives of exponential functions and the exponential model
Reviewing the chain rule and the derivatives and limits of trigonometric functions
Review of the limit definition of a derivative and calculating the derivative
Review of derivatives and tangent lines to functions and vector equations
Proving a property of scalar multiplication for limits using the epsilon-delta definition and using the Squeeze Theorem for Limits.
Approximation and Newton's Method, and limits and derivatives of exponential functions
Limits at infinity and asymptotes, along with physics applications
Limits at infinity, asymptotes, and tangent lines
Review of the limit definition of a derivative and calculating the derivative
Review of derivatives and tangent lines to functions and vector equations
Differentials, linear approximations and quadratic approximations
Review of the limit definition of a derivative and calculating the derivative
Derivatives and tangents to curves
Derivatives of trigonometric functions and using the Chain Rule
Approximation and Newton's Method, and limits and derivatives of exponential functions
Derivatives of trigonometric functions and using the Chain Rule
Derivatives and vectors with some physics applications
Derivatives of exponential and logarithmic functions and the exponential model
Using derivatives to find properties of graphs
Using derivatives to find properties of graphs
Using L'Hospital's Rule to solve limits
Using u substitution to evaluate integrals and prove facts about logarithms and integrals and
Proving the Fundamental Theorem of Calculus and examples of u Substitution
Interpreting integrals to represent areas between curves
Proving trigonometric identities useful for integration
Using trigonometric identities to integrate powers of sine and cosine
Explaining the cases for using trigonometric substitution
Finding a partial fraction decomposition and integrating using partial fractions
Evaluating a double integral over a rectangle
Determining if a sequence is increasing, decreasing, or not monotonic and if it is bounded
Using a rotation map matrix to rotate a 2-dimensional vector by the angle \(\pi\)
Finding the six trigonometric ratios for a right triangle
Using trig to find an angle in a right triangle with two given sides
Explaining the special right triangles and the relationships between their sides
Finding the values of trig functions with the unit circle
Finding the exact value of secant, cosecant, and cotangent using the unit circle
Finding the exact values of cosine and cotangent for given angles using the unit circle
Finding the exact values of sine and secant for several given angles using the unit circle
Finding the angles where sine has a given value using the unit circle
Finding the angle where secant has a given value and tangent is positive
Using the unit circle to sketch the graph of the sine function
Using the unit circle to sketch the graph of the cosine function
Graphing a period of a transformed sine function
Graphing a period of a transformed cosine function
Writing the sine and cosine functions for a given graph
Using the reciprocal and ratio trig identities to simplify an expression
Using the Pythagorean Identities to simplify a trig expression
Using the Pythagorean Trig Identity to derive the secondary Pythagorean Identities
Using the sum identities of sine and cosine to derive the double angle identities
Using the difference identities of sine and cosine to derive the cofunction identities
Using the double angle identities for cosein to derive the half-angle identities for sine and cosine
Using the Sum and Difference Identities to find the exact value of cosine
Using the Sum Identity for Trig to find the exact value of sine
Using a Double Angle Identity to find the exact value of an expression with sine and cosine
Using the Reciprocal, Ratio, and Pythagorean Identities to verify a trig identity
Proving a trigonometric identity involving secant, cotangent, and tangent
Proving a trig identity involving sine and cosine
Proving a trig identity involving sine, cosine, and cotangent
Finding all solutions to a trigonometric equation with sine
Solving a trigonometric equation with sine and cosine by factoring
Solving a trigonometric equation with secant by factoring
Using the Even/Odd and Cofunction Identities to solve an equation with sine
Solving a trig equation with sine and cosine using aPythagorean Identity
Solving a trig equation with cotangent and cosecant using trig identities
Solving a trig equation with sine and cosine using trig identities
Solving a trig equation with cosine using trig identities
Solving a trig equation with cotangent and sine using trig identities
Finding the values of \(\theta\) that makes a matrix with trig functions invertible
Determining whether trigonometric functions are linearly independent
Finding the dimension of the subspace spanned by a set of functions
Using trigonometry to determine the edge lengths of a right triangle
Writing the equation of a line passing through two points
Writing the equation of a line through two points in slope-intercept form
Writing the equation of a graphed line in standard form
Factoring a quadratic polynomial
Factoring a quadratic function
Factoring a cubic polynomial by grouping
Finding the greatest common factor of a polynomial and then factoring it out
Factoring a quadratic where the leading coefficient is 1
Factoring quadratics where the leading coefficient is not 1
Factoring several polynomials by grouping
Factoring a difference of two squares
Factoring a sum of cubes and a difference of cubes
Simplifying a rational expression
Adding and then simplifying two rational expressions
Multiplying two rational expressions and then simplifying
Dividing rational expressions and then simplifying the answer
Adding two rational expressions and then simplifying the answer
Finding any holes, vertical asymptotes, and horizontal asymptotes of a rational function
Finding any holes, vertical asymptotes, and horizontal asymptotes of a rational function
Matching a rational function with its graph
Using the quadratic formula to find the roots of a function
Finding the roots of a cubic polynomial
Finding the roots of a square root function
Finding the roots of a function with an absolute value
Finding the domain of a rational function
Finding the domain of a rational function
Finding the domain of a function with a fraction and radicals
Finding the domain of a function with a quadratic inside a square root
Finding the composition of two functions
Finding the composition of a rational function and a quadratic
Finding the composition of two functions with exponentials and logarithms
Finding the composition of two functions with a square root and a fractional exponent
Finding the composition of two functions with a cube root and a fractional exponent
Finding the inverse of a linear function and its domain
Finding the inverse of a square root function and its domain
Finding the inverse of a rational function and its domain
Finding the inverse of a rational function and its domain
Finding and simplifying the difference quotient for a quadratic function
Finding and simplifying the difference quotient for a rational function
Finding and simplifying the difference quotient for a square root function
Solving an inequality with a polynomial by factoring and using a sign diagram
Solving an inequality with a rational expression by factoring and using a sign diagram
Solving an inequality with two rational expressions using a sign diagram
Solving an inequality with a rational expression using a sign diagram
Solving an inequality with a quadratic by factoring and using a sign diagram
Finding the absolute maximum or absolute minimum of a quadratic
Writing the standard form of quadratic function given its vertex and one other point
Finding the component form and magnitude for a vector between two points
Performing calculations with vectors including addition, subtraction, and scalar multiplication
Calculating the dot product for three pairs of vectors
Finding a unit vector in the direction of a given vector
Solving a system of two linear equations using the method of substitution
Solving a system of two linear equations using the method of substitution
Solving a system of two linear equations
Solving a system on two equations where one is linear and one is quadratic
Solving a equation with an exponential function
Solving an equation with two exponential functions with different bases
Solving an equation with exponential functions by factoring
Solving a equation with exponential functions by factoring
Finding the size of a population of rabbits with exponential growth
Finding the size of a population of rabbits with exponential decay
Finding the horizontal asymptote of an exponential function
Finding the horizontal asymptote of an exponential function
Finding the horizontal asymptote of an exponential function
Expanding a logarithmic expression using logarithm properties
Condensing logarithmic expressions into a single logarithm
Finding the exact value of logarithms using logarithmic properties
Finding the vertical asymptote of a logarithmic function
Finding the vertical asymptote of a logarithmic function
Finding the domain and x-intercepts of a logarithmic function
Finding the domain and x-intercepts of a logarithmic function
Solving a logarithmic equation using properties of logarithms
Solving a logarithmic equation using properties of logarithms
Sketching one period of a cosine function with transformations
Solving equations symbolically in Python and interpreting the results
Review of the limit definition of a derivative and calculating the derivative