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Inverse Trig Functions for csc-1, sec-1, and cot-1

Learn how to find the exact values and solve problems using the inverse trig functions csc-1, sec-1, and cot-1. Create triangles when the given values don't correspond to the unit circle. Practice with examples.

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Inverse Trig Functions for csc-1, sec-1, and cot-1

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  1. Chapter 7 Analytic Trigonometry

  2. Section 2The Inverse Trigonometric Functions (continued)

  3. In 7.1, we defined quadrants and intervals for sin-1, cos-1, and tan-1 We still need to do the same thing for csc-1, sec-1, and cot-1

  4. csc-1x (csc is the reciprocal of sin) will only exist in quadrants I and IV -/2 ≤ ≤ /2; ≠ 0 sec-1x (sec is the reciprocal of cos) will only exist in quadrants I and II 0 ≤ ≤ 2; /2 cot-1x (cot is the reciprocal of tan OR cos/sin) will only exist in quadrants I and II 0 ≤ ≤ 2

  5. Find exact values: cot-1 sec-1 csc-1(-1)

  6. Example: cos(sin-1 () ) Tan(cos-1()) Sin-1(sin())

  7. What if the given values don’t correspond to the values on the unit circle? When in doubt, create a triangle!

  8. Example: tan(sin-1(1/3)) 1/3 doesn’t exist on the unit circle  draw a triangle  sin-1 is in quadrants I or IV  1/3 is positive, so start in quadrant _____

  9. Example: sec(tan-1(-1/2))

  10. EXIT SLIP

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