12) y = -2 sin 1 2 x - 2

Transcription

1 Review -Test 1 - Unit 1 and - Math 41 Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Find and simplify the difference quotient f(x + h) - f(x), h 0 for the given function. h 1) f(x) = x + 7x + Use periodic properties of the trigonometric functions to find the exact value of the expression. 10) sin Use a vertical shift to graph the function. 11) y = cos x - 1 Write the partial fraction decomposition of the rational expression. ) x - x - 17 x - x ) x + x - x + x 4) 8x + 7x - 7 x + x + x + ) x + x + (x + 4) 1) y = - sin 1 x - 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. ) - 9, Find sin t. Solve the problem. 7) What is the range of the sine function? Use even and odd properties of the trigonometric functions to find the exact value of the expression. 8) cos - 0 t < and cos t is given. Use the Pythagorean identity sin t + cos t = 1 to find sin t. 9) cos t = 1

2 1) y = - cos x - + 1) y = 1 4 cot x Graph the function. 14) y = tan x Use the graph to obtain the graph of the reciprocal function. Give the equation of the function for the graph that you obtain. 17) y = 1 sin 1 x 1) y = tan x + Graph the function. 18) y = sec x

3 19) y = csc x + 9) sin x - cos x sin x + cos x - sin x cos x =? Find the exact value by using a sum or difference identity. 0) cos (1 + 0 ) Find the exact value of the expression. 1) cos 0 cos 40 - sin 0 sin 40 Complete the identity. sin ( - ) ) cos cos =? Find the exact value of the expression. 0) sin -1 0 Use the given information to find the exact value of the expression. ) tan =, lies in quadrant III, and cos = - 1 1) cos -1 -, lies in quadrant II Find sin ( + ). ) tan -1 (-1) Find the exact value of the expression, if possible. Do not use a calculator. ) cos -1 cos 4) tan =, lies in quadrant III Find sin 1. Express the sum or difference as a product. ) cos x x + cos 4) tan -1 tan 7 Use a sketch to find the exact value of the expression. ) cos tan -1 ) sec tan -1 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. 7) tan(sec -1 x + ) x Complete the identity. sin x + sin x ) cos x + cos 4x =? Find all solutions of the equation. 7) 9 cos x + = 7 cos x+ 8) tan x sec x = - tan x Solve the equation on the interval [0, ). 9) cos x = 40) sin x - cos x = 0 Complete the identity. csc x cot x 8) =? sec x 41) sec x - = tan x

4 4) sin x + sin x = 0 Solve the equation on the interval [0, ). 4) cos x + cos x sin x = 0 Solve the equation on the interval [0, ). 44) sec x = cos x 4) cos x + sin x - = 0 4) cos x = - cos x 47) sin x sin x - 11 = 1 4

5 Answer Key Testname: REVIEW - TEST 1 MATH 41 FALL 01 1) x + h + 7 ID: PCALCZ 1..- ) 17 x + - x x - 1 ID: PCALCZ ) x + - x (x - 1) 4) ) ID: PCALCZ x + + 4x - x + ID: PCALCZ x x - (x + 4) ID: PCALCZ ) 1) ID: PCALCZ 4..- ) ID: PCALCZ ) all real numbers from -1 to 1, inclusive ID: PCALCZ ) 9) 10) - 11) ID: PCALCZ ID: PCALCZ ID: PCALCZ ) ID: PCALCZ ID: PCALCZ 4..- ID: PCALCZ 4..-4

6 Answer Key Testname: REVIEW - TEST 1 MATH 41 FALL 01 1) 18) 1) ID: PCALCZ ) ID: PCALCZ 4..- ID: PCALCZ ) y = 1 csc 1 x ID: PCALCZ ) 0 ID: PCALCZ ) ID: PCALCZ ) - 4 ID: PCALCZ ) ID: PCALCZ ) - 7 ID: PCALCZ ID: PCALCZ ) 1 1 ID: PCALCZ

7 Answer Key Testname: REVIEW - TEST 1 MATH 41 FALL 01 ) 7) x ID: PCALCZ ID: PCALCZ ) cot x ID: PCALCZ ) - sec x csc x ID: PCALCZ ) - 1) 1 ( + 1) 4 ID: PCALCZ..- ID: PCALCZ..-8 ) tan - tan ID: PCALCZ..-1 ) - ID: PCALCZ..-4 4) ID: PCALCZ..1-4) 0,, ID: PCALCZ..-8 4),,, 11 ID: PCALCZ..4-44) 0 ID: PCALCZ..- 4) 0,,, ID: PCALCZ..-7 4) 8, 7 8, 9 8, 1 8 ID: PCALCZ..- 47) ID: PCALCZ..-11 ) cos x cos x ) ID: PCALCZ.4.-8 sin 4x cos x ID: PCALCZ ) x = 4 + n or x = 4 + n ID: PCALCZ ) x = + n or x = + n or x = n ID: PCALCZ ) 8, 7 8, 9 8, 1 8 ID: PCALCZ..- 40) 4, 4, 4, 7 4 ID: PCALCZ ) no solution ID: PCALCZ..-4 7