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NAME DATE 4-6 PERIOD Practice Inverse Trigonometric Functions Sketch the graph of each function. 1. y = arccos 3x 2. y = arctan x + 1 y π π π 2 y π 2 1x 0.5 -1 -0.5 0 -2 -1 -π 2 -π -π 4. y = tan −1 3x 3. y = sin −1 3x π 2x 1 0 -π 2 y π y π 2 π 2 -1 -0.5 0 1x 0.5 -2 -1 -π 2 -π -π 2x 1 0 -π 2 Find the exact value of each expression, if it exists. √3 2 ) ( 3π 7. tan − − 2 ( ) π −− √3 3 ) 3 2) π 8. sin −1 cos − ) π − 3 3 √3 3 − 3 6 1 10. arcsin − − π -− ( √3 3 ( 2) 6 ( π − ( π −− 1 11. tan sin -1 1 - cos -1 − ) ( undefined 9. arctan - − π 6. cos −1 cos − 6 ) 12. sin arctan − − 1 −− 2 13. ART Hans purchased a painting that is 30 inches tall that will hang 8 inches above the fireplace. The top of the fireplace is 55 inches from the floor. a. Write a function modeling the maximum viewing angle θ for the distance d for Hans if his eye-level when sitting is 2.5 feet above the ground. (d) (d) 63 33 θ = tan −1 − − tan −1 − b. Determine the distance that corresponds to the maximum viewing angle. 46.6 in. Write each trigonometric expression as an algebraic expression of x. 14. sin (arccos x) Chapter 4 √ 1 - x2 x √ 1 - x2 1-x 15. tan (sin −1 x) − 2 34 Glencoe Precalculus Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. ( 5. arcsin −1 - −