; approximate b to the nearest tenth and B or β to the nearest minute. Hint: Draw a triangle. B = = B. b cos 49.7 = 215.

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1 M 1500 am Summer 009 1) Given with 90, c 15.1, and α 9 ; approimate b to the nearest tenth and or β to the nearest minute. Hint: raw a triangle. b 18., b 19.9, 0 58 b b 1.0, 0 18 cos b 1.0, 0 58 b b 15.1cos(9.7 ) b 19.1, 0 18 b ) measure the height of a large billboard in Times Square in New York ity, two sightings 500 feet along a street from below the billboard are taken. The angle of elevation to the bottom of the billboard is 55 and the angle of elevation to the top of the billboard is 1 0'. What is the height of the billboard to the nearest foot? 07 ft. 79 ft. 0 ft. 19 ft. None of the bove. tan 55 h b tan 55 h b h tan ( 1.5 ) tan(1.5 ) h 500 tan(55) 500 tan(1.5) b (substitution) b 500(tan(1.5) tan(55)) b 0.8 h b ) Ship leaves port at :00 PM and sails in the direction S at a rate of 5 miles per hour. The second ship,, leaves the port at :0 PM and sails in the direction N 7 at a rate of 0 miles per hour. What is the heading from ship to ship at :00 PM? S19 W N S 8 W N19 N Port θ heading θ θ 5 tan θ 19 N 19 1

2 M 1500 am Summer 009 ) man and his son are playing paintball. The man is on the roof of a building and wants to hit his son who is standing on the ground. The angle of depression from the man s paint gun to his son s feet is 5 and the height from the base of the building to the man's paint gun is 8 feet. How far will the paint ball travel through the air from the paint gun until it hits the feet of the son? ssume the paint ball travels in a straight line. Round to the nearest tenth of a foot.. ft. 5. ft. 0.0 ft. 0.9 ft. None of the bove. 5) Find all solutions of the equation below using n as an arbitrary integers. cos α α + n, + n 5 α + n, + n α + n, + n 5 α + n, + n None of the bove. 5 d α cos 1 1 cos α 1 cosα ± 8 cos(5 ) d 8 d cos(5 ) d 0.9 ft. α + n and α + n α will be in all quadrants with a reference angle of ) Find all solutions in the interval [0, ) for the equation below. How many solutions are there? Reference angle is in Q II and Q IV(tan is 1 tan negative). Terminal sides are in opposite directions. Use 5 + n equal to angle. 5 + n n -1 / 5 + n 0 / solutions 1 7/ + n 5/

3 M 1500 am Summer 009 7) Which statement is false? Use your knowledge of the sum/difference formulas, double-angle formulas, cofunction formulas, and/or inverse trig functions. cot( 0 ) tan( 0 ) sin θ sin cosθ cos sinθ tan 55 tan 5 tan tan(5 ) tan(0 ) sin sin cos 5 arcsin sin The false one is the one with tangent or 55. The numerator should have a + and the denominator a to be the sum of two angles tangent formula. 8) Find the eact value of sin(10 5 ). + + sin(10) cos(5) cos(10) sin(5) Remember: The sin is positive in Q II and negative in Q III; the cos in negative in both these quadrants. 1 9) If α and β are acute angles such that value of cos( α β ). 7 sin α and cos β 5 1 1, find the eact None of the bove. 5 7 α cosα cos β + sinα sin β β 5 1

4 M 1500 am Summer ) Find the eact solutions of the equation below in the interval [0, ). sin t sin(t) 0 t 0,,, 5 t,,, 5 t 0,,, 5 t, None of the bove. sin t sin t cos t 0 sin t(1 cos t) 0 sin t 0 1 cost 0 1 cost 5 t 0, t, (-1,0) (1,0) 11) If a projectile is fired from ground level with an initial velocity of v feet per second and at an angle of θ degrees with the horizontal, the range R of the v projectile is given by R sinθ cosθ. If v 90 feet per second, approimate 1 the angle(s) that result(s) in a range of 00 feet. Round to the nearest tenth of a degree. θ 5. θ.1, θ 11., 78. θ. 1) The epression.9 None of the bove. sin cos sinθ cosθ ()sinθ cosθ sin( θ ) θ θ θ.1 θ.9 is equivalent to which of the following? sin sin cos sin cos sin sin sin ( sin cos ) cos cos sin cos cos sin

5 M 1500 am Summer ) Find the eact value of the following: sin 1 cos sin cos sin (Inverse sin returns a negative value as a negative angle in Q IV.) 1) Use the quadratic formula (and an inverse trigonometric function) to approimate the solutions of the following equation in the interval [0, ) to three decimal places. heck mode on calculator. sin + sin ,.95.59,.0 No solution. None of the bove. ± 1 ()( 1) ± 8 sin () sin sin 1.58 R (This is impossible) R 5

6 M 1500 am Summer ) Which is the graph of y cos? 1 1 The domain of the function has been doubled. The domain is [-, ]. The range of an inverse cosine function is [0, ]. The graph that fits on this form of the eam is.