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Test 2 - Math 2412 Name___________________________________ Chapter 4 and 5 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Use a vertical shift to graph the function. 6) y = -3 sin 2x + The point P(x, y) on the unit circle that corresponds to a real number t is given. Find the value of the indicated trigonometric function at t. 5 2 6 ,Find csc t. 1) 7 7 Solve the problem. 2) What is the domain of the sine function? Determine the phase shift of the function. 1 3) y = -5 sin x 2 2 Determine the amplitude or period as requested. 1 4) Period of y = -5 cos x 2 Graph the function. x 7) y = 4 tan 2 Graph the function. 2 5) y = - cos 2x + 3 2 8) y = 2 cot x + 1A 4 2 -2 Solve the equation on the interval [0, 2 ). 3 18) cos 2x = 2 Use the graph to obtain the graph of the reciprocal function. Give the equation of the function for the graph that you obtain. 9) y = 3 cos 2 x Find the exact value of the expression. 19) cos (160°) cos (40°) + sin (160°) sin (40°) Use the given information to find the exact value of the expression. 3 2 20) sin = , lies in quadrant II, and cos = , 5 5 lies in quadrant I Use a half-angle formula to find the exact value of the expression. 21) sin 22.5° Find the exact value of the expression. 2 10) cos-1 2 Solve the equation on the interval [0, 2 ). 22) sin 3x = 0 11) tan-1 0 Use the given information to find the exact value of the trigonometric function. 3 lies in quadrant IV Find 23) sin = - , 5 Use a sketch to find the exact value of the expression. 3 12) cos tan-1 8 sin Use a right triangle to write the expression as an algebraic expression. Assume that x is positive and in the domain of the given inverse trigonometric function. x2 + 4 ) 13) tan(sec -1 x (sin x + cos x)2 =? 1 + 2 sin x cos x 15) sin x + cos x cos x - sin x =? sin x cos x 2 . Use the given information to find the exact value of the expression. 20 , lies in quadrant IV Find sin 2 24) cos = 29 . Complete the identity. 14) Find cos ( - ). Express the product as a sum or difference. 25) sin 7x sin 3x The point P(x, y) on the unit circle that corresponds to a real number t is given. Find the value of the indicated trigonometric function at t. 3 2 10 ,Find csc t. 26) 7 7 Solve the equation on the interval [0, 2 ). 16) sin2 x + sin x = 0 Find the exact value of the trigonometric function. Do not use a calculator. Solve the equation on the interval [0, 2 ). 17) (tan x + 1) (sin x + 1) = 0 27) -tan 2 4 + 19 Use even and odd properties of the trigonometric functions to find the exact value of the expression. 28) cos (-150°) 34) y = 2 sec x 3 Sin t and cos t are given. Use identities to find the indicated value. Where necessary, rationalize denominators. 3 2 10 . Find tan t. 29) sin t = , cos t = 7 7 Use a calculator to find the value of the trigonometric function to four decimal places. 30) cot 10 35) y = 6 csc x + Determine the phase shift of the function. 1 31) y = 5 sin x 4 4 2 Graph the function. 32) y = -2 sin (3 x + 2) Find the exact value of the expression, if possible. Do not use a calculator. 36) cos-1 cos 33) y = -tan x + 6 Use a sketch to find the exact value of the expression. 3 73 37) cot sin-1 73 2 Use a right triangle to write the expression as an algebraic expression. Assume that x is positive and in the domain of the given inverse trigonometric function. x2 + 4 ) 38) sin(sec-1 x Use substitution to determine whether the given x-value is a solution of the equation. 4 2 3 , x= 39) sin x = 3 3 3 Find all solutions of the equation. 40) 5 sin x - 5 3 = 3 sin x- 4 3 Solve the equation on the interval [0, 2 ). 2 41) cos 2x = 2 42) cos2 x + 2 cos x + 1 = 0 43) sin2 x - cos2 x = 0 Solve the equation on the interval [0, 2 ). 44) tan2 x sin x = tan2 x Solve the equation on the interval [0, 2 ). 45) tan 2x - tan x = 0 46) cos x + 4 - cos x - 4 =1 Use a calculator to solve the equation on the interval [0, 2 ). Round the answer to two decimal places. 47) sin x = -0.37 Use a calculator to solve the equation on the interval [0, 2 ). Round to the nearest hundredth of a radian. 48) cos 2x - cos x = 0 Find the exact value of the expression, if possible. Do not use a calculator. 49) cos-1 cos - 6 4 Answer Key Testname: REVIEW TEST 2 - CH 4 TO 5 - MATH 2412 - 1) - 8) 7 6 12 2) all real numbers 3) units to the right 4) 4 5) 9) y = 3 sec 2 x 6) 10) 3 4 11) 0 8 73 12) 73 7) 13) 2 x 14) 1 15) sec x csc x 3 16) 0, , 2 17) 18) 12 19) - 5 , 4 , 2 , 4 11 13 23 , , 12 12 12 1 2 20) -8 + 3 21 25 21) 1 2 2- 2 Answer Key Testname: REVIEW TEST 2 - CH 4 TO 5 - MATH 2412 - 22) 0, 3 , 23) 10 10 24) - 840 841 25) 34) 2 4 5 , , , ,2 3 3 3 1 (cos 4x - cos 10x) 2 26) - 7 10 20 27) -1 28) 29) 3 2 35) 3 10 20 30) 3.0777 31) units to the right 32) 36) 33) 6 37) 8 3 38) 2 x2 + 4 x2 + 4 39) No 40) x = 41) 8 4 + 2n or x = , 7 9 15 , , 8 8 8 , 3 5 7 , , 4 4 4 42) 43) 3 44) 0, 45) 0, 46) 4 , 4 47) 3.52, 5.90 48) 0, 2.09, 4.19 6 3 + 2n Answer Key Testname: REVIEW TEST 2 - CH 4 TO 5 - MATH 2412 - 49) 6 7