Chapter 6: Inverse Circular Functions and Trigonometric Equations

2 (some quadrantal angles have only 1)

for any non-quadrantal given trigonometric function value, there are ___ angles within the range [0, 2π)

range

if an operation is done on the variable in the original problem, change the ____________ according to the operation done

where n is any integer (and use n in the rest of the answer before)

if no range is specified in the original trigonometric equation, use this phrase at the end of the answer

y = sin⁻¹x, y = csc⁻¹x, y = tan⁻¹x

inverse functions for which the interval is [-π/2, π/2] aka quadrants I and IV

y = cos⁻¹x, y = sec⁻¹x, y = cot⁻¹x

inverse functions for which the interval is [0, π] aka quadrants I and II

inverse

remember to check along the way for if the range requirement is met when solving equations involving ________________ functions

y (check range though)

tan⁻¹(tan y)

y = arc sin x, x = sin y (for -π/2 ≤ y ≤ π/2)

two other ways to write y = sin⁻¹x

T (if not in the original equation, you have to add or subtract values in your calculator to get the second value)

T or F? The rules for the range of inverse functions ONLY apply when the inverse function is in the original problem

x

cos(cos⁻¹x)