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14.3 Converting Between Degrees and Radians and Inverse Trigonometry

14.3 Converting Between Degrees and Radians and Inverse Trigonometry. Converting Between Degrees and Radians. When we convert between degrees and radians we multiply by a . The easiest value that is equivalent is radians and degrees.

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14.3 Converting Between Degrees and Radians and Inverse Trigonometry

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  1. 14.3 Converting Between Degrees and Radians and Inverse Trigonometry

  2. Converting Between Degrees and Radians • When we convert between degrees and radians we multiply by a . • The easiest value that is equivalent is radians and degrees. • So, to convert from degrees to radians we multiply by . • And to convert from radians to degrees we multiply by . 1 π 180º

  3. Convert each angle measure from degrees to radians. 1. 2. 3.

  4. Convert each angle measure from radians to degrees. Round to the nearest tenth. 4. 5. 6.

  5. Revolutions Greater than a Full Circle • The unit circle continues to revolve past a full circle in both the positive and the negative direction. • An is determined by rotating a ray about its vertex. • The of an angle is the ray extending from the vertex before rotation. • The resulting ray, after the rotation, is called the . • When the initial side coincides with the positive x-axis and the vertex is at the origin, it is said to be in • . angle side initial side terminal position standard

  6. In order to evaluate trig functions of angles larger than one revolution, it is helpful to determine where on the unit circle the value lies by working backwards. • To find that value, you can subtract a full circle until you get a value that is on the first revolution.

  7. Sketch the angle in standard form and evaluate the trig function. 7. 8.

  8. Sketch the angle in standard form and evaluate the trig function. 9. 10.

  9. Sometimes you will be given the value of the trigonometric function and you will need to work backwards to find the point on the unit circle that corresponds to that value. • Typically you will be looking at one revolution of the unit circle – so between 0 and in radians and between 0° and 360° in degrees.

  10. Find θsuch that . 11. • Is positive or negative? • In which quadrant(s) is the sin value positive? • What real number, θ, has a y-coordinate of ?

  11. Find θsuch that . 12. • Positive or negative? • What quadrant(s) is secant negative in? • What is the reciprocal of ? • What real number, , has an x-coordinate of ?

  12. Find θsuch that . 13. • Positive or negative? • What quadrant(s) is tangent positive in? • Where is tangent equal to ?

  13. Find θsuch that . 14. • Positive or negative? • What does this mean about sin? • Where is sinθ = 0?

  14. Use the unit circle below to help remember when each trig function is positive.

  15. Find θsuch that . 15. 16. 17. 18.

  16. Find θsuch that . 19. 20. 21. 22.

  17. Evaluate. 23. 24. 25. 26.

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