MA 1032 Review for exam III
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1 MA 10 Review for eam III Name Establish the identit. 1) cot θ sec θ = csc θ 1) ) cscu - cos u sec u= cot u ) ) cos u 1 + tan u - sin u 1 + cot u = cos u - sin u ) ) csc θ + cot θ tan θ + sin θ = csc θ cot θ ) Write the trigonometric epression as an algebraic epression in u. ) sin (tan-1 u) Find the eact value of the epression. ) cos sin-1 1 7) cos-1 sin 7π Find the eact solution of the equation. 8) sin-1 = π Find the inverse function f-1 of the function f. 9) f() = cos + 8 Find the eact value of the epression. Do not use a calculator. 10) cos-1 cos - π Use a calculator to find the value of the epression rounded to two decimal places. 11) cos-1 7 1) tan-1(1.) 1) sin-1(0.7) 1
2 Graph the function. Show at least one period. 1) = sin( - π) 8 -π π π π ) = cos + π 8 -π π π π Find the phase shift. 1) = sin 1 - π 17) = - cos 1 + π
3 Find an equation for the graph. 18) 1 -π -π -1 π π ) 1 -π -π -1 π π Use transformations to graph the function. 0) = - cos -π -π π π -
4 1) = sin 1 -π -π π π - Use the even-odd properties to find the eact value of the epression. Do not use a calculator. ) sin (-0 ) Find the eact value of the indicated trigonometric function of θ. ) tan θ = - 10, θ in quadrant II Find cos θ. 7 In the problem, sin θ and cos θ are given. Find the eact value of the indicated trigonometric function. ) sin θ =, cos θ = Find cot θ. Name the quadrant in which the angle θ lies. ) sin θ > 0, cos θ < 0 Use the properties of the trigonometric functions to find the eact value of the epression. Do not use a calculator. ) sin 70 + cos 70 A point on the terminal side of an angle θ is given. Find the eact value of the indicated trigonometric function of θ. 7) (-, -) Find cos θ. Find the eact value. Do not use a calculator. 8) cos 1π 9) tan 0 0) cos In the problem, t is a real number and P = (, ) is the point on the unit circle that corresponds to t. Find the eact value of the indicated trigonometric function of t. 1) (, 7 ) Find tan t.
5 ) ( 11, ) Find sec t. If A denotes the area of the sector of a circle of radius r formed b the central angle θ, find the missing quantit. If necessar, round the answer to two decimal places. ) r = inches, θ = radians, A =? Convert the angle in degrees to radians. Epress the answer as multiple of π. ) Convert the angle in radians to degrees. ) 10 π If s denotes the length of the arc of a circle of radius r subtended b a central angle θ, find the missing quantit. ) r = 11.0 inches, θ = 0, s =? Solve the problem. 7) The half-life of plutonium- is 9 hours. If 0 milligrams is present now, how much will be present in das? (Round our answer to three decimal places.) 8) The size P of a small herbivore population at time t (in ears) obes the function P(t) = 700e0.1t if the have enough food and the predator population stas constant. After how man ears will the population reach 100? 9) Sand manages a ceramics shop and uses a 00 F kiln to fire ceramic greenware. After turning off her kiln, she must wait until its temperature gauge reaches 190 F before opening it and removing the ceramic pieces. If room temperature is 70 F and the gauge reads 00 F in 8 minutes, how long must she wait before opening the kiln? Assume the kiln cools according to Newton's Law of Cooling: U = T + (U0 - T)ekt. (Round our answer to the nearest whole minute.) Solve the equation. Epress irrational answers in eact form and as a decimal rounded to decimal places. 0) = 1 - Solve the equation. 1) log ( + ) - log ( - ) = log ) log( - ) - log( - ) = Write as the sum and/or difference of logarithms. Epress powers as factors. ) log Epress as a single logarithm. ) log a + log a ( - ) + log a
6 Use the Change-of-Base Formula and a calculator to evaluate the logarithm. Round our answer to two decimal places. ) log
7 Answer Ke Testname: 10 EXAM III REVIEW 1) cot θ sec θ = cos θ sin θ 1 cos θ = 1 sin θ = csc θ ) cscu - cos u sec u = cscu - cos u ) ) cos u 1 + tan u - sin u 1 + cot u = cos u 1 + sin u cos u (cos u - sin u)(cos u + sin u) cos u + sin u csc θ + cot θ tan θ + sin θ = 1 sin θ + cos θ sin θ = sin θ cos θ + sin θ 1 cos u = csc u - 1 = cotu sin u cos u = sin u = cos u - sin u 1 + cos θ sin θ sin θ + sin θ cos θ cos θ cos u cos u + sin u - sin u sin u + cos u = cos u - sin u cos u + sin u = = 1 + cos θ sin θ cos θ sin θ(1 + cos θ) = 1 sin θ cos θ sin θ = csc θ cot θ ) u u + 1 u + 1 ) 7) π 8) = 9) f-1() = cos ) π 11) 0.9 1) )
8 Answer Ke Testname: 10 EXAM III REVIEW 1) 8 -π π π π - 1) π π π π ) π units to the right 17) π units to the left 18) = sin () 19) = - cos () 0) -π -π π π - 8
9 Answer Ke Testname: 10 EXAM III REVIEW 1) -π -π π π - ) - 1 ) ) ) II ) 1 7) - 8) - 1 9) 0) 1) 7 ) ) in ) π ) 00 ).8 in. 9
10 Answer Ke Testname: 10 EXAM III REVIEW 7) ) 7.8 r 9) 7 min ln 0) ln + ln ) {9} ) {} ) log - log ) log a ( 0-0) ).9 10
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