Prof. Israel N. Nwaguru MATH 11 CHAPTER,,, AND - REVIEW WORKOUT EACH PROBLEM NEATLY AND ORDERLY ON SEPARATE SHEET THEN CHOSE THE BEST ANSWER TO EARN ANY CREDIT, YOU MUST SHOW STEPS LEADING TO THE ANSWER MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the corresponding angle measure in radians. 1) -10 1) D) Convert the degree measure to radians. Leave answer as a multiple of. ) 88 ) 1 D) ) 10 ) 17 17 17 D) 17 Find the exact value without using a calculator. ) csc ) - - 1 - D) - ) sec ) - - D) - Find the length of an arc intercepted by a central angle in a circle of radius r. Round your answer to 1 decimal place. ) r = 11.19 in.; = 19 ) 9.0 in. 78.1 in. 19.0 in. D).8 in. 1
7) r = 1.0 cm.; = radians 7). cm 1. cm 7. cm D) 1. cm Find the exact circular function value. 8) tan 7 8) - D) Use a table or a calculator to evaluate the function. Round to four decimal places. 9) sec 0.00 9) 0.9797 0.00 0.08 D) 1.008 Find the value of s in the interval [0, /] that makes the statement true. Round to four decimal places. 10) cos s = 0.78 10).80 0.8 0.7 D) 0.98 11) tan s = 7.7 11).88 1. 0.80 D) 1.00 Use the formula = t to find the value of the missing variable. Give an exact answer unless otherwise indicated. ) = 1.077 radians per min, = 10.77 radians (Round to four decimal places when necessary.) ) 11.87 min 9.99 min 0.1 min D) 11.07 min Give the amplitude or period as requested. 1) Amplitude of y = cos 1 x 1) D) Find the specified quantity. 1) Find the vertical translation of y = - + sin x +. 1) up down up D) up 1 1) Find the period of y = - cos 1 x +. 1) 8 D) Graph the function over a one-period interval.
1) y = + 1 sin (x - ) 1) D) Graph the function.
17) y = cot x + 17) D)
18) y = - - tan x + 18) D)
19) y = 1 csc x + 19) D)
0) y = - sec x - 0) D) Use the fundamental identities to find the value of the trigonometric function. 1) Find sec if tan = and is in quadrant I. 1) - - 7 9 D) 7 7 7
) Find tan if sin = and is in quadrant II. ) - 7 7 - D) - 7 9 ) Find cos if csc = - and is in quadrant IV. ) - 11 D) 9 9 ) Find csc if cot = - 1 and is in quadrant II. ) - 1 D) - 1 ) Find sin if cot = - and cos < 0. ) - 1 - D) Complete the sentence so the result is an identity. Let x be any real number. ) 1 + = cscx ) cosx sinx cotx D) secx 7) sin x tan x = 7) cos x cot x csc x D) sec x 8) - 1 = tanx 8) sinx cotx secx D) cosx 9) + tanx = secx 9) sinx cosx -1 D) 1 0) cos x = (cot x)( ) 0) sin x tan x sec x D) csc x 1) sin x = ( )(cos x) 1) csc x cot x sec x D) tan x Write the expression in terms of sine and cosine, and simplify so that no quotients appear in the final expression. ) tan x(cot x - cos x) ) 1 - sin x 0 1 D) - sec x ) csc x cot x sec x sec x 1 csc x D) cot x ) 8
) tan sec cos sin tan D) sec ) ) sin x - 1 cos (-x) sin x -sin x cos x D) -cos x ) Perform the indicated operations and simplify the result so there are no quotients. sin ) 1 + sin - sin 1 - sin sin tan sec csc - tan D) 1 + cot ) 7) sin cos + cos sin 1 + cot - tan sin tan D) sec csc 7) 8) tan - sin tan sec 8) 1 + cot sin tan - tan D) sec csc Factor the trigonometric expression and simplify. 9) secx - secx tanx + tanx 9) secx (1 + tanx) secx + tanx D) 1 0) secx + secx tanx - tanx 0) secx + tanx - 1 secx - D) secx 1) tanx - secx 1) secx secx + tanx - tanx - 1 D) tan - secx Use the fundamental identities to simplify the expression. ) sin x(cot x + 1) ) 1-1 tan x D) cos x + 1 ) cos x sin x + cos x sec x ) cot x csc x csc x D) sec x ) cos x (csc x - sec x) - cot x ) cosx - tanx 0-1 D) 1 ) cos (-x) cos x - sin (-x) sin x ) cosx sinx 0 D) 1 9
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Verify that each equation is an identity. ) cotx = (csc x - 1)(csc x + 1) ) 7) (sec - tan )(sec + tan ) = 1 7) 8) sec + tan = cos 1 - sin 8) 9) sec - 1 tan = tan sec + 1 9) 0) 7 csc - cot = csc + 0) 1) 1- sec tan + tan = - csc 1) 1 - sec MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use Identities to find the exact value. ) cos (-1 ) ) - - + D) - - ) cos ) - + - D) - - ) cos cos - sin sin ) 1 D) 1 ) cos 7 cos + sin 7 sin ) 1-1 D) Write in terms of the cofunction of a complementary angle. ) tan 0 ) cot 0 cot - 0 tan - 0 D) cot 0 7) sin 87 7) csc csc 9 cos D) cos 9 10
Tell whether the statement is true or false. 8) cos 17 7 = cos 9 cos 8 - sin 9 sin 8 8) True False 9) cos = cos 9 cos 7 - sin 9 sin 7 9) True False Use a sum or difference identity to find the exact value. 0) tan 7 0) - - - + - D) + 1) sin 1 cos 10 + cos 1 sin 10 1) - 1 D) - 1 ) tan 80 + tan 70 1 - tan 80 tan 70 ) - 1 - - D) - ) sin 7 ) + 1 - + D) 1 Using a sum or difference identity, write the following as an expression involving functions of x. ) tan (0 + x) ) tan x - 1 + tan x tan x -tan x D) 1 + tan x - tan x SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Verify that the equation is an identity. ) tan x - = tan x - 1 1 + tan x ) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the exact value by using a half-angle identity. ) sin 7 ) - 1-1 - 1 + D) - 1 + 7) cos. 7) - 1 + 1 + 1 - D) - 1-11
Find the exact value of the real number y. 8) y = cos-1 8) 11 D) 9) y = arcsin - 9) 7 - D) Solve the equation for exact solutions over the interval [0, ). 70) cos x = sin x 70), 7, 7, D), 71) secx - = tanx 71) D) 7) sinx + sin x = 0 7) 0,,, 0,,, 0,, D) 0,,, 7) sinx - cosx = 0 7),, D),,, 7 Solve the equation for exact solutions. 7) cos -1 x = 7) 1 D)
Answer Key Testname: M11-CH-REVIEW-HCC-FALL 01 1) B ) A ) C ) D ) C ) A 7) C 8) D 9) D 10) B 11) B ) B 1) D 1) B 1) C 1) B 17) A 18) D 19) C 0) B 1) A ) A ) B ) A ) D ) C 7) A 8) C 9) D 0) A 1) D ) A ) D ) B ) D ) C 7) D 8) C 9) D 0) C 1) C ) A ) C ) C ) D ) cot x = csc x - 1 = (csc x - 1)(csc x + 1). 7) (sec - tan )(sec + tan ) = sec - tan = 1 8) sec + tan = 1 sin 1 + sin 1 + sin 1 - sin + = = cos cos cos cos 1 - sin = 1 - sin cos (1 - sin ) = 1 cos cos (1 - sin ) = cos 1 - sin
Answer Key Testname: M11-CH-REVIEW-HCC-FALL 01 9) sec - 1 tan = sec - 1 tan sec + 1 sec + 1 = sec - 1 tan (sec + 1) = tan tan (sec + 1) = tan sec + 1 0) 7 csc - cot = csc + csc - cot = csc + (csc - cot ) = csc + 1) 1- sec tan + tan 1 - sec = (1 - sec ) + tan = 1 - sec + sec + tan = sec - sec tan (1 - sec ) tan (1 - sec ) tan (1 - sec ) = sec ( sec - 1) tan (1 - sec ) = - sec tan = - cos cos sin = - = - csc sin ) D ) B ) B ) A ) B 7) C 8) A 9) B 0) D 1) A ) C ) C ) D ) tan x - = tan x - tan / 1 + (tan x)(tan /) = tan x - 1 1 + tan x. ) C 7) B 8) D 9) B 70) C 71) D 7) C 7) D 7) D 1