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)