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Hour: _____ Name: ___________________________ Date: ____________________________ PreCalculus: Chapter 4 Practice Test (1) 1. Indicate whether each is True or False. 4 _____ a) cot 3 3 _____ b) sin 2 _____ c) cos 1 1 0 _____ d) csc _____ e) 2 3 cos 0 _____ f) cot sec 5 12 csc sec sin 2 2 ______ h) For 3 , tan tan . 2 2 2 sec 1 7 7 ______ j) cos 15 1 sec15 ______ g) sin ______ i) tan 12 sin 2 ______ k) If cos 0 and sin 0 , then 3 2 . 2 2. Evaluate the other five trigonometric functions of if sec 3.5 and csc 0 . 3. Let f TRIG where TRIG can be replaced by any of the six trigonometric functions. Which function(s) could replace TRIG in each situation? 4 4 a) f 1 b) f f 4 3 3 c) f 1 2 6 d) f 0 for 2 e) f f 2 f) The domain of f is , . g) f 3 f 3 4 h) 2 f 6 f 6 4 i) f co-f , where co-f is the cofunction of f . 2 j) f 1 , where co-f is the cofunction of f . co-f 4. Verify. 1 sin 1 sin a) 1 sec tan sec tan b) sec tan c) 1 sin x cos x 2sec x cos x 1 sin x d) 1 sec2 sin csc sin e) 1 1 2sec 2 1 sin 1 sin f) csc 4 csc 2 cot 4 cot 2 2 5. Let f x x3 2 x and g x sin x . Show that all the zeros of f are also zeros of g . 6. Identify all asymptotes and intercepts of the rational function f x 2 x 2 10 x 12 . x3 10 x 2 24 x 7. Identify all asymptotes and intercepts on the interval 0, 2 of the trigonometric function f x tan x . 8. From a point 150 ft in front of a building, the angles of elevation to the top of the building and to the top of the flagpole atop the building are 42° and 47°, respectively. Draw a figure. Label the height of the building and the flagpole with appropriate variables. Find the height of the flagpole to the nearest tenth of a foot. 9. Explain why each of the following is not possible. 8 3 a) It is given that sin and tan . 10 4 b) It is given that cos 5 and tan 0 . 4 c) It is given that sin 10. Given cos 8 and the terminal side of lies in Quadrant II. 19 8 , evaluate tan using two methods. 17 a) Right triangle trigonometry b) A Pythagorean identity 11. Find all values of on the interval 0, 2 such that cos 0.2725 . 12. Find all values of x on the interval 0, 2 such that csc x 1.3784 . 13. A tunnel for a highway is to be cut through a mountain, which is 14,411 feet high. At a distance of 2 miles from the base of the mountain, the angle of elevation to the summit is 36. From a distance of one and a half miles on the opposite side of the mountain, the angle of elevation is 47. Find the length of the tunnel to the nearest foot. 36 2 mi 47 1.5 mi