WIR5 20B M150 V4
Evaluating all six trigonometric functions for angles in degrees and radians
Solving Equations Symbolically in Python
Author: David Manuel
In this video, it is shown how to solve equations symbolically using Python and save the results as variables to use the results in furthur calculations. We also learn how to recognize when Python is giving a small imaginary part due to round off errors. The example given in the video solves a trigonometric equations, and it is shown how to convert the radian answers into degrees.
Transcript 04
Transcript 04
Problem: Suppose former A&M punter Braden Mann wants to punt a ball 50 m and the ball leaves his foot with an initial velocity of 30 m/s. To determine the angle the ball needs to be kicked, it can be shown that the answer can be found by solving the equation \[50\tan(\theta)-\dfrac{13.61}{\cos(\theta)^2} = 0.\]
Python Code:
from sympy import *
theta=symbols('theta')
LHS=50*tan(theta)-13.61/(cos(theta))**2
thsol=solve(LHS,theta)
angle1=re(thsol[2])
angle2=re(thsol[3])
print(angle1*180/pi.evalf(),angle2*180/pi.evalf())
Open Python Notebook File
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WIR 20B M152 V51
Determining if a series converges or diverges
WIR 20B M152 V57
Using the comparison test to determine if a series converges or diverges
WIR 20B M152 V58
Using the comparison test to determine if a series converges or diverges
WIR 20B M152 V64
Using the Alternating Series Test to determine if a series converges or diverges
Introduction and Installation of Python
An introduction to installing and getting started with Python
Numerical Calculations in Python
Performing basic numerical calculations in Python
Plotting Expressions and Solving Equations Numerically in Python
Plotting an expression in Python and finding a numerical approximation for the solution
Plotting Multiple Expressions in One Graph in Python
Graphing a piecewise function using Python
Creating and Manipulating Symbolic Expressions in Python
Creating symbolic expression in Python and then factoring, expanding, and simplifying the expressions
Using Variables in Python
Defining variables in Python and using the variables in equations
Simplifying Difference Quotients in Python
Using Python to simplify a difference quotient and find a derivative using the limit definition
Word Problems and the Algorithmic Process for Multistep Problem Solving in Python
Solving a multistep word problem in Python and graphing the resulting function
Tangents to Parametrized Curves at a Given Point in Python
Using Python to plot a parametrized curve and its tangent line at a point
Definite and Indefinite Integrals in Python
Solving definite and indefinite integrals in Python
Finding Absolute (Global) Extrema in Python
Using Python to find the absolute maximum and minimum of a function on a closed interval
Finding and Graphing Tangent Lines to a Curve in Python
Using Python to find the equation of the tangent line to a curve and graphing the result
Finding Derivatives in Python
Finding derivatives in Python and solving for the rate of change of a force
Finding Horizontal Tangent Lines in Python
Finding when the tangent line to a function is horizontal in Python
Finding Intervals of Increase/Decrease and Concavity in Python
Using Python to find the intervals where a function is increasing or decreasing
Parametric Plots and Tangents at a Given t-value in Python
Using Python to find the tangent line to a parametric equation and plot the two graphs
List Comprehension and Numerical, Graphical, and Symbolic Limits in Python
Using Python to numerically estimate a limit, graphically estimate a limit, and find the exact limit
List Comprehension and Patterns in Higher Derivatives in Python
Using Python's list comprehension tool to find several higher order derivatives of a function at once
Implicit Plots and Implicit Differentiation in Python
Using Python to plot an implicit curve and find a tangent line using implicit differentiation
Approximating Definite Integrals with Riemann Sums in Python
Using Python to approximate a definite integral using left endpoint Riemann sums
Areas Between Curves in Python
Using Python to identify the region between curves and then evaluate the area of the region
Calculating Work in Python: Hooke’s Law
Using Python to calculate the amount of work done in moving a spring using Hooke's Law
Calculating Work in Python: Pumping Liquid from a Tank
Using Python to calculate the work done in pumping the liquid from a tank whose ends are semicircles
Plotting a Function and Partial Sums of its Power Series in Python
Video 29 in a series of Python instructional videos
Radius and Interval of Convergence in Python
Using Python to find the radius and interval of convergence of a power series with the Ratio Test
For Loops and Recursive Sequences in Python
Using for loops in Python to generate a recursively defined sequence
Generating and Plotting Partials Sums of a Series in Python
Using Python to calculate the partial sums of a series to estimate the value of the series
Generating and Plotting Sequences in Python
Using Python to numerically, graphically, and analytically find the limit of a sequence
Volumes of Revolution in Python
Finding the volume of a solid of revolution in Python
Review for the Common Exam: MATH 151 Exam 1 Review Problems 10-13
Review of vector functions and parametric equations
Review for the Common Exam: MATH 151 Exam 1 Review Problems 26-35
Review of the limit definition of a derivative and calculating the derivative
Review for the Common Exam: MATH 151 Exam 3 Review Problems 8-15
Review of limits and derivatives of inverse trigonometric functions