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Section 4.4 – Trigonometric Functions of Any Angle

Section Details.
  • Using a point on the terminal side of any angle to define the six trigonometric functions
  • Learning in which quadrant each trigonometric function is positve and negative
  • Definition of reference angle
  • Using the reference angle and the quadrant to evaluate trigonometric functions of any angle
  • Evaluating the trigonometric functions for an angle when given some information about the angle


Practice Problems


Directions. The following are review problems for the section. We recommend you work the problems yourself, and then click "Answer" to check your answer. If you do not understand a problem, you can click "Video" to learn how to solve it. 
  1. Let \((-24, 7)\) be a point on the terminal side of \(\theta\).  Find the sine, cosine, and tangent of \(\theta\). 

    \(\sin\theta=\dfrac{7}{25}\)
    \(\cos\theta=-\dfrac{24}{25}\)
    \(\tan\theta=-\dfrac{7}{24}\)


    To see the full video page and find related videos, click the following link.
    WIR5 20B M150 V9

  2. Let \((3, -8)\) be a point on the terminal side of \(\theta\).  Find the sine, cosine, and tangent of \(\theta\). 

    \(\sin\theta=-\dfrac{8}{\sqrt{73}}\)
    \(\cos\theta=\dfrac{3}{\sqrt{73}}\)
    \(\tan\theta=-\dfrac{8}{3}\)


    To see the full video page and find related videos, click the following link.
    WIR5 20B M150 V10

  3. Given \(\displaystyle{\sin (\theta) = -\frac{5}{7}}\) and \(\displaystyle{ \tan ( \theta ) > 0}\), find \(\displaystyle{\tan ( \theta )}\) and \(\displaystyle{ \sec( \theta ) }\).

    \(\tan\theta=\dfrac{5}{2\sqrt{6}}\)
    \(\sec\theta=-\dfrac{7}{2\sqrt{6}}\)


    To see the full video page and find related videos, click the following link.
    WIR5 20B M150 V11

  4. Find the reference angle for:
    1. \(\theta=330^\circ\)
    2. \(\theta=\cfrac{7\pi}{4}\)
    3. \(\theta=\cfrac{13\pi}{9}\)
    4. \(\theta=-255^\circ\)

      1. \(30^\circ\)
      2. \(\dfrac{\pi}{4}\)
      3. \(\dfrac{4\pi}{9}\)
      4. \(75^\circ\)

      To see the full video page and find related videos, click the following link.
      WIR5 20B M150 V12