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Name: Hour: Date: Honors Pre-Calculus: Chapter 4 Practice Test (1) 1. Indicate whether each is True or False. a) cot ( 471- b) (sin 0)2 = sin2 0 = 3I 571. r d) csc— = sec12 12 c) cos-1 1= 0 e) < 0 < 37z- —> cos 0 < 0 g) — sin — 71- = sin 2 i) tan 2 2r 2r =sec 1 7 7 f,) cot 0 = csc sec q$ h) For r <0 < 37r , tan 0 = tan (0— ). 2 j) cos(-15°) = 1 sec15° 371. k) If cos 0 > 0 and sin 0 < 0 , then — < 0 <2r . 2 2. Evaluate the other five trigonometric functions of 0 if sec 0 = —3.5 and csc 0 > 0. 3 I. 7 3. Let f(0) =TRIG 0 where TRIG can be replaced by any of the six trigonometric functions. Which function(s) could replace TRIG in each situation? ( r 47r \ b) f a) f — =1 =-f 3 ) 4) tOkn C., c) f y (2) = C d) f (0)> 0 for 5 ( A C e) f (0) = f (0 —2g) f) The domain of f(0) is (—G0,09). I' A JI g) f (0 +37r) = f (0) h) —2f 6) I\ ( 0 71. f(0) = co-f -- j) f(0) = , where co-f is the cofunction of f. 1 , where co-f is the cofunction of f . cof (0) f ( 67T 4 II 4. Verify. a) 1 - sec 0 + tan 0 sec 0 - tan 0 1 2 b) (sec - tan 0) - sin 1+ sin 0 1 - f - 7- -\\ - 421/ 3 c) 1 + sin x cos x 1 1- cos x = 2sec x . l+sinx •Y, AY .4-6) ' 0—c 7 ,K d) sin 0 (csc - sin 0) = sec 2 0 ro< V\ X '1 .1" e) 1 1 = 2 sec2 + 1-sin01+sin0 f) csc4 0 - csc2 0 = cot4 0 + cot2 0 c5(z 6) t)(9-k - tA 5. Let f (x) = x3 — 7r 2x and g (x) = sin x . Show that all the zeros of f are also zeros of g. 0 2x 2—10x +12 6. Identify all asymptotes and intercepts of the rational function f (x) — 3 X — 1 OX 2 — 24x 0 1,1 V 1(A. O a ( V .- 0 () 0 0 I Act f(-o) uno ,i 7. Identify all asymptotes and intercepts on the interval [0,27r) 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. 4 9. Explain why each of the following is not possible. 8 a) It is given that sin a = — and tan a = 10 4 5 b) It is given that cos p = - and tan 4 <0. 8 c) It is given that sin 0 = -- and the terminal side of0 lies in Quadrant II. 19 8 10. Given cos 0 = — , evaluate tan 0 using two methods. 17 a) Right triangle trigonometry b) A Pythagorean identity 1/ 11. Find all values of 6' on the interval [0,27r) such that cos 0 = 0.2725. 1, (796 z. /7 C 12. Find all values of x on the interval [0,27r) such that csc x = —1.3784. S 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. (-1 14 -cA .n366 t n- MOP