1 / 22

4.4 Trigonmetric functions of Any Angle

4.4 Trigonmetric functions of Any Angle. Objective. Evaluate trigonometric functions of any angle Use reference angles to evaluate trig functions. Definitions of Trigonometric Functions of any Angle.

kamilah
Download Presentation

4.4 Trigonmetric functions of Any Angle

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 4.4 Trigonmetric functions of Any Angle

  2. Objective • Evaluate trigonometric functions of any angle • Use reference angles to evaluate trig functions

  3. Definitions of Trigonometric Functions of any Angle • Let θbe an angle in standard position with (x, y) a point on the terminal side of θ and

  4. The cosecant function is the reciprocal of the sine. • The secant function is the reciprocal of the cosine. • The cotangent function is the reciprocal of the tangent function.

  5. Example 1 • Let (-3, 4) be a point on the terminal side of θ. Find the sine, cosine, and tangent of θ.

  6. Example 2 • Let (2, 5) be a point on the terminal side of θ. Find the sine, cosine, and tangent of θ.

  7. Signs of the Trigonometric Functions

  8. Signs of the Trig Functions A means that all trig. functions are positive.S means that all sine and cosecant functions are positive.T means that all tangent and cotangent functions are positive.C means that all cosine and secant functions are positive.

  9. Example 3 • State whether each value is positive, negative, or zero. • a) cos 75° positive • b) sin 3π 0 • c) cos 5π negative • d) sin(-3π) 0

  10. Example 4 • Given.

  11. Example 5 • Angle θis in standard position with its terminal side in the third quadrant. Find the exact value of cos θif

  12. Example 6 • Angle θ is in standard position with its terminal side in the fourth quadrant. Find the exact value of sin θ if

  13. Reference Angles • Definition • Let θ be an angle in standard position. Its reference angle is the acute angle θ’ formed by the terminal side of θand the horizontal axis.

  14. Reference angles

  15. Example 7 • Finding reference angles.

  16. Trigonometric Values of Common Angles

  17. Example 8 • Use the reference angle to find sin θ, cos θ, and tan θ for each value of

  18. Example 9 • Determine the values of θ for which

  19. If the value of one of the trig functions of any angle is known, a calculator can be used to determine the angles having that value.

  20. Example 10 • Find values of θ, where • to the nearest tenth of a degree.

  21. Example 11 • Find values of θ, where • To the nearest hundredth of a radian.

More Related