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Academy Algebra II 13.4: Evaluate Inverse Trigonometric Functions (PC 4.7) HW: p.878 (3-10 all, 16-24 even, 27-31 all, 35, 36) Inverse Trig Functions • Inverse function is denoted by: 1 y arcsin x or y sin x • arcsin x means the angle whose sine is x. (same meaning as inverse) Evaluate the expression without using a calc. 1 1.) (a) arccos 2 1 1 2.) (a) cos 2 (b) arccos 0 (b) sin 1 2 2 Use a calculator to approximate the value. 3.) (a) arcsin( 0.75) (b) cos 1 (0.7) 4.) (a) tan 1 0.98 (b) arctan 4.7 Use an inverse trig function to write as a function of x. Example: A swimming pool is 20 meters long and 12 meters wide. The bottom of the pool has a constant slant so that the water depth is 1.3 meters at the shallow end and 4 meters at the deep end. Find the angle of depression of the bottom of the pool. Pre-Calc book: p.353 (70) Find the exact value of each of the remaining trig functions of . 3 1.) cos , is in Quadrant IV 5 2 2.) sin , 180 270 3 3.) sec 2, sin 0 4.) cot 2, sec 0 Use a calculator to approximate two values of . 0 360 1.) sin 0.8191 2.) tan 0.6524 3.) sec 1.2241 4.) cos 0.9848 PC Book: Find the two solutions of the equation. Give your answers in both degrees and radians. Do not use a calculator. 1 2 79a.) sin 80a.) cos 2 2 2 3 81a.) csc 3 81b.) cot 1 2 3 83a.) sec 3 1 83b.) cos 2 PC Book: Find the indicated trig value in the specified quadrant. 3 97.) sin ; Quadrant IV; Find cos 5 98.) cot 3 ; Quadrant II; Find sin 3 99.) tan ; Quadrant III; Find sec 2 100.) csc 2 ; Quadrant IV; Find cot Pre-Calc book: p.354 (77) Pre-Calc book: p.312 (65) Pre-Calc book: p.312 (68)