INVERSE TRIG FUNCTIONS

Inverse Functions Must pass the horizontal line test. Can be written sin -1 or arcsin, cos -1 or arccos, and tan -1 or arctan Used to find angles. Ex. arcsin ( )= ____ Means find the angle whose sine is

EASY EXAMPLES… Evaluate using a calculator. Round to two decimals (Radian Mode). 1. arccos ( ) 2. arcsin ( ) 3. arctan.98

The RULES Sin x: can only lie in Quad I and IV sin(arcsin x) = x and arcsin(sin x) = x Cos x: can only lie in Quad I and II cos(arccos x) = x and arccos(cos x) = x Tan x: can only lie in Quad I and IV (cannot be on y-axis) tan(arctan x) = x and arctan(tan x) = x

HINT OF THE DAY RE-MEMORIZE YOUR UNIT CIRCLE

Use Properties to Evaluate 1. arcsin(sin ) 2. arccos(cos ) 3.sin -1 (sin ) 4.tan -1 (tan 120 °)

Use Properties to Evaluate 5. arcsin(sin ) 6. arccos(cos 300 °) 7. cos -1 (cos ) 8. tan -1 (tan )

Use an inverse trig function to write θ as a function of x. (SOLVE FOR θ ) x 4 x+1 10 θ θ

Find all sides of the right triangle 11. θ = arcsin, find cos θ and tan θ. ? ? ? θ

Find the exact value of the expression. SET UP A RIGHT TRIANGLE 12. cot(cos -1 )

13. cos(tan -1 ) 14. cot(sin -1 )

Find the exact value of the expression. 15. csc(arcsec x)