C) ) cos (cos-1 0.4) 5) A) 0.4 B) 2.7 C) 0.9 D) 3.5 C) - 4 5

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1 Precalculus B Name Please do NOT write on this packet. Put all work and answers on a separate piece of paper. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the exact value of the expression. 1) sin-1 3 1) A) 3 B) 3 C) 3 D) ) cos-1 3 ) A) B) 11 6 C) 7 D) 6 3) tan ) A) 5 B) 3 C) 6 D) 5 6 Find the exact value of the expression, if possible. Do not use a calculator. ) cos-1 cos - 3 ) A) 3 B) 3 C) - 3 D) 3 5) cos (cos-1 0.) 5) A) 0. B).7 C) 0.9 D) 3.5 Use a sketch to find the exact value of the expression. 6) cos sin ) A) B) 1 5 C) - 5 D) 5 Complete the identity. 7) csc x(sin x + cos x) =? 7) A) sin x tan x B) 1 + cot x C) sec x csc x D) - tan x 8) sin x + sin x cot x =? 8) A) cot x - 1 B) cot x + 1 C) 1 D) sin x + 1 9) sin x - cos x sin x + cos x - sin x cos x =? 9) A) 1 - sec x csc x B) sec x csc x C) - sec x csc x D) + sec x csc x 1

2 Use the given information to find the exact value of the expression. 10) Find cos ( - ). sin = 5, lies in quadrant II, and cos =, lies in quadrant I. 10) 5 A) B) C) D) Find the exact value by using a sum or difference identity. 11) sin 15 11) A) - ( 3 + 1) B) ( 3 + 1) C) ( 3-1) D) - ( 3-1) Find the exact value of the expression. 1) cos 15 cos 5 - sin 15 sin 5 1) 3 A) B) 3 C) 1 D) 1 Find the exact value by using a difference identity. 13) tan ) A) B) + 3 C) - 3 D) + 3 Use the given information to find the exact value of the expression. 1) Find sin. tan = 1, lies in quadrant III. 1) 0 A) B) C) 1 81 D) Write the expression as the sine, cosine, or tangent of a double angle. Then find the exact value of the expression. 15) cos 10 - sin 10 15) A) - 1 B) 1 C) - 3 D) 3 Find all solutions of the equation. 16) cos x + = 0 16) A) x = + n or x = 7 + n B) x = + n or x = 7 + n C) x = 3 + n or x = 5 + n D) x = 3 + n or x = 5 + n 17) tan x sec x = - tan x 17) A) x = 3 + n or x = n or 0+ n B) x = 3 + n or x = 3 C) x = 3 + n or x = n or 0 + n D) x = 3 + n or x = 3 + n or 0 + n + n or 0 + n

3 Solve the equation on the interval [0, ). 18) cos x = A) 8, 7 8, 9 8, 15 8 C) 0, 3,, 3 B), 3, 5, 7 D) no solution 18) 19) sin x = sin x 19) A), 3, 3, 3 B) 0,, 6, 5 6 C) 3, 3 D) 6, 5 6 0) sec x - = tan x 0) A) 3 B) C) no solution D) 6 1) cos x + sin x - = 0 1) A), 3, 3, 3 B) 0,, 6, 5 6 C) 3, 3 D) 6, 5 6 Using a calculator, solve the following problems. Round your answers to the nearest tenth. ) A ship leaves port with a bearing of N W. After traveling 15 miles, the ship then turns 90 and travels on a bearing of S 6 W for 13 miles. At that time, what is the bearing of the ship from port? A) N 0.9 W B) N 8.9 W C) N 67.9 W D) N 3.1 W ) Two sides and an angle (SSA) of a triangle are given. Determine whether the given measurements produce one triangle, two triangles, or no triangle at all. Solve each triangle that results. Round lengths to the nearest tenth and angle measures to the nearest degree. 3) B = 31, b = 1, a = 6 3) A) A = 9, C = 119, c = 0 B) A = 7, C = 11, c = 37 C) A = 30, C = 10, c = 1.5 D) none of the above ) C = 35, a = 18.7, c = 16.1 ) A) A1 = 103, B1 =, b1 = 7.; B) A =, B = 103, b = 7. A = 7, B = 138, b = 3. C) A1 =, B1 = 103, b1 = 7.; D) no triangle A = 138, B = 7, b = 3. Solve the triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. 5) b = 7, c = 8, A = 109 5) A) a = 18, B = 31, C = 0 B) a = 15.1, B = 35, C = 36 C) a = 1., B = 33, C = 38 D) no triangle 6) a = 8, b = 5, c = 6) A) A = 15.1, B =.1, C = 30.8 B) A = 30.8, B =.1, C = 15.1 C) A = 15.1, B = 30.8, C =.1 D) A = 30.8, B = 15.1, C =.1 3

4 Solve the problem. 7) Two airplanes leave an airport at the same time, one going northwest at 09 mph and the other going east at 35 mph. How far apart are the planes after hours (to the nearest mile)? A) 6 miles B) 13 miles C) 716 miles D) 679 miles 8) Two points A and B are on opposite sides of a building. A surveyor selects a third point C to place a transit. Point C is 5 feet from point A and 69 feet from point B. The angle ACB is 53. How far apart are points A and B? A) 56.5 feet B) 73.7 feet C) feet D) 99.6 feet 7) 8) Polar coordinates of a point are given. Find the rectangular coordinates of the point. 9) 9, 3 9) A) 9, -9 3 B) - 9, 9 3 C) - 9, -9 3 D) 9, 9 3 The rectangular coordinates of a point are given. Find polar coordinates of the point. 30) (-, - ) 30) A) (, 135 ) B) (8, 5 ) C) (8, 135 ) D) (, 5 ) The graph of a polar equation is given. Select the polar equation for the graph. 31) 31) A) r = sin B) r sin = 1 C) r = 1 D) r = cos

5 3) 3) A) r = cos( ) B) r = sin( ) C) r = + cos( ) D) r = Graph the polar equation. 33) r = 1 + sin 33) 5

6 3) r = cos ( ) 3) Write the complex number in rectangular form. 35) 7(cos 3 + i sin 3 ) 35) A) i B) + -7 i C) i D) i Find the product of the complex numbers. Leave answer in polar form. 36) z1 = 5(cos 3 + i sin 3 ) z = 3(cos 18 + i sin 18 ) A) 15(cos 16 + i sin 16 ) B) 15(cos 5 + i sin 5 ) C) 8(cos 5 + i sin 5 ) D) 8(cos 5 + i sin 5 ) 36) Find the quotient z 1 of the complex numbers. Leave answer in polar form. z 37) z1 = i z = i A) C) 3 (cos 7 + i sin 7 ) B) 3 (cos 7 - i sin 7 ) 3 (cos - i sin ) D) 3 (cos + i sin ) 37) 6

7 Use DeMoivre's Theorem to find the indicated power of the complex number. Write answer in rectangular form. 38) (- + i 3) 3 38) A) 6 B) - + i 3 C) 6 + 1i 3 D) 51 Find all the complex roots. Write the answer in the indicated form. 39) The complex square roots of 36(cos 60 + i sin 60 ) (polar form) 39) A) 6(cos 30 + i sin 30 ), 10(cos 10 + i sin 10 ) B) 6(cos 60 + i sin 60 ), -6(cos 10 + i sin 10 ) C) 6(cos 60 + i sin 60 ), 6(cos 10 + i sin 10 ) D) 6(cos 30 + i sin 30 ), 6(cos 10 + i sin 10 ) 0) The complex cube roots of 8i (rectangular form) 0) A) -i, 3 + i, i B) i, 3 + i, i C) -i, i, 3 - i D) i, 3 - i, i A vector v has initial point P1 and terminal point P. Write v in terms of ai + bj. 1) P1 = (1, 3); P = (-3, 3) 1) A) v = - j B) v = -i C) v = j D) v = i Find the specified vector or scalar. ) u = -i - j, v = 6i + 7j; Find u - v. ) A) -1i + 5j B) i + 5j C) -10i - 9j D) -11i + 5j 3) v = -7i + 10j; Find -5v. 3) A) 5 51 B) 5i 51 C) 5 19 D) Use a vertical shift to graph the function. 7

8 ) y = - sin 1 x + ) 8

9 5) y = -3 sin x + 3-5) 9

10 6) y = - tan x 6) 10

11 7) y = - cot (x + ) 7) 11

12 8) y = sec x + 8) 1

13 9) y = - 1 csc x 9) 13