Analytic Trigonometry Chapter 7 Analytic Trigonometry

Section 2 The Inverse Trigonometric Functions (continued)

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

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

Find exact values: cot-1 − 3 sec-1 2 3 3 csc-1(-1)

Example: cos(sin-1 ( 2 2 ) ) Tan(cos-1(− 3 2 )) Sin-1(sin( 7𝜋 6 ))

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

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 _____

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

EXIT SLIP