MA 154 PRACTICE QUESTIONS FOR THE FINAL 11/ The angles with measures listed are all coterminal except: 5π B. A. 4

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1 . If θ is in the second quadrant and sinθ =.6, find cosθ The angles with measures listed are all coterminal except: E. 6. The radian measure of an angle of is: 7. Use a calculator to find the sec 6 correct to decimal places

2 . The point (, 6) is on the terminal side of the angle θ. Find tanθ 6. If the diameter of a circle is 6 cm, find the length of the arc that subtends a central angle of..7 cm.6 cm. cm. cm 7. Find the area of a sector determined by θ in problem #6..7 cm.6 cm. cm. cm. Sketched below is a portion of the graph of which trigonometric function? y = cos x y = cos( x) y = cos( x) y = cos x E. y = cos( x)

3 . The graph of y = + sin x (Choose all the correct answers.) I. crosses the y-axis at II. crosses the x-axis at multiples of III. is always above the x-axis IV. has period I, II I, III, IV I, II, IV II, IV. Give the domain, D, and the range, R, of f(x) = cos x. D = set of all real numbers, R=[, ] D = [, ), R = set of all real numbers. D = [, ], R = [, ] D = set of all real numbers, R = [, ]. From a point P on level ground the angle of elevation of the top of the tower is 6 '. From a point. meters closer to the tower and on the same line with P and the base of the tower, the angle of elevation of the top of the tower is '. Find the height of the tower correct to one decimal place.. meters.6 meters 7. meters.7 meters. The expression tan x + sec x is equal to: sec x tan x + sin x tan x + sin x tanx E. csc x + sin x

4 . Simplify tan x cosx csc x cot x sec x sin x. tan x cos x csc x E. tan x. Reduce to a single term: cos(a) cos B + sin (A) sin. Find all the solutions of cos x + sin x + = in the interval [, ) sin (A + B) sin (A B) cos (A B) cos (A + B) x =, x =, x = x = 6. How many solutions of the equation sinθ = cosθ lie in the interval [, )?

5 7. Find cosθ in the given triangle. θ E. None of the above. Given cosθ = and 7 < θ < 6, find sinθ Which equation best describes the graph given below? y = sin ( x) x y = cos y = cos ( x) x y = sin

6 . Find the cos arcsin. Do not use a calculator Point A is. miles north of The bearing from A to C is S W and the bearing from B to C is S 6 W. Find the distance from A to C correct to one decimal place..6 miles.6 miles. miles. miles. Find the magnitude of the vector, 6 6. If a =, and b =,, the sketch below corresponds to: a + b (6, ) a b a + b a b 6

7 . If 6. lb, is the magnitude and direction of one force and. lb, is the magnitude and direction of a second force, calculate the magnitude (to one decimal place) and the direction (to the nearest degree) of the resultant.. lb, 7. lb,. lb, 7. lb,. Which equation best describes that graph given below? y (, ) ( x 6) x 6 ( ) ( + y ) = ( + y ) = (6, ) x E. ( x ) x ( ) ( x ) ( + y ) = ( + y ) = ( + y ) = 6. Classify the equations given below. I. x y + x = II. x + y + x y = III. x x + y 7 = I. ellipse II. parabola III. hyperbola I. hyperbola II. ellipse III. parabola I. parabola II. hyperbola III. ellipse I. hyperbola II. parabola III. ellipse E. I. parabola II. ellipse III. hyperbola F. I. ellipse II. hyperbola III. parabola 7

8 7. The graph of x y = most closely resembles which graph sketched below? E. F Find the vertex of the parabola y y x = (, ) (, ) (, ) (, ). An arch of a bridge over a roadway is semi elliptical with major axis horizontal. The base of the arch is feet across and highest part of the arch is feet above the horizontal roadway. Find the height of the arch feet from the center of the base.. feet. feet 7. feet. feet

9 . What are the vertical asymptotes of the graph of f (x) = x x + x?. The graph of f (x) = x x + x = x = x =, x = x =, x = most closely resembles which graph sketched below? A E.. Find the reference angle for θ = 6 θ R = 6 θ R = θ R = 66 θ R =. Find the reference angle for θ = θ R = θ R = θ R = θ R =. Find all the values of θ in the interval [, ) that satisfies the equation sin θ =.7. Round your answer to two decimals..6,.77.6,..77,.66.,.

10 . Sketched below is a portion of the graph of which trigonometric function? y = sin x + y = sin x y = sin x + y = sin x + E. y = sin x 6. Find the unit vector that is in the same direction as i j. i + j i j i j i + j 7. Find the vector of magnitude that is in the opposite direction of, 7., 6 6,, 6 6,

11 Answers: C B E A C D C D E (-/) A 6 A C 7 B 6 B C 7 A B B A C C C B D B D C A E (/) C 6 C A 7 D 6 C A 7 A B