Math 60 Final Review (Sponsored by The Learning Center). Simplify cot csc csc. Prove the following identities: cos csc csc sin. Let 7sin simplify.. Prove: tan y csc y cos y sec y cos y cos sin y cos csc tan. Make the trigonometric substitution into cot y tan 9 and 5. Evaluate the following eactly, using an addition/subtraction formula: cos95 6. Evaluate cos cos sin sin 8 9 8 9 sin using an addition/subtraction formula. 7. Evaluate sin cos tan
8. Given that sin Quadrant III, find the following eactly:, where is in Quadrant II, and tan, where is in sin cos cos 9. Given that, find the following eactly: sin, where and tan sin cos, where c) cos d) sin e) Quadrant for? f) Quadrant for? 0. Evaluate the following eactly using a double or half-angle formula. cos.5 c) sin 8 e) cossin. Prove the following: 5 d) sin cos 5 5 cos sin cos cos y sin sin y cos y sin cos sec sin cos. Solve, finding all solution in 0, : cos cos sin sin
c) cos 0. Solve, finding all solution in 0, : sin sin cos 0 sin 0 c) tan sec. Solve the following systems of equations y 5 y 9 5y 55y 5. A man invests his savings in two accounts, one paying 6% interest per year and the other paying 7%. He has twice as much invested in the 7% account as in the 6% account, and his annual interest income is $600. How much is invested in each account? 6. Find the complete solution of the linear system, or show that it is inconsistent. For infinite solutions, write your answer in parametric form. y z y z 6 y 7. Use the rules of eponents to simplify. No negative eponents y y y y 8. Perform the following operation and simplify: y y 9. Solve: 0 5 6 5 6
c) Solve: 5 0. Evaluate the epression an write in standard form, a + bi: i 9 i. Solve. Write your answer in standard form, a + bi:. Solve: a. 5 t 0. t 6 8 7 7 0 y c.. Test the equation for symmetry:. Let f Find the domain of f. f c) f h d) f 7 e) f 0 5. Let f. Write an equation for the transformed function when one shifts units right and reflects across the y-ais. 6. Let F, G, and H 5 following and their domains.. Find the F G ( FG)( ) H G c) d) F G e) H H f) H F
g) F H h) G H 7. Use the functions below to find: g if if f f g f g c) g f 5 if if 8. Find the inverse of the one-to-one function. Give the domain and range of both f and f : f f 6 9. Find the domain and range of 0. For the polynomial function, find (i) degree, (ii) leading coefficient, (iii) end behavior, (iv) the zeros and their multiplicity, (v) the y-intercepts, and (vi) sketch the graph. 5 k. For the following polynomial, find all zeroes (real and comple) and factor completely. 5 P
. For the following rational function, find (i) domain, (ii) holes (if any), (iii) vertical asymptotes (if any), (iv) horizontal or oblique asymptotes (if any), (v) intercepts, and (vi) sketch the graph:. Solve the following inequality:. Solve the rational inequality: 5. Find the domain of f f 5 8 0 6 6. For the following eponential function, find (i) domain, (ii) range, (iii) intercepts, (iv) asymptotes, and (v) sketch the graph: h f e 7. Sketch the function of the horizontal asymptote. 5. Find the intercepts, range, and the equation 8. Evaluate the following without a calculator: log 6 ln e 9. For the following logarithmic function, find (i) domain, (ii) range, (iii) intercepts, (iv) log asymptotes, and (v) sketch the graph: h 0. Find the inverse of f ln. Convert each equation into eponential or logarithmic form. log 8 6. Evaluate the epression log 6 e 0.
. Use the Laws of Logarithms to epand the epression:. Use the Laws of Logarithms to combine the epression: log5 log5 log5 5. Solve the following equations: 9 c) log log ln d) Solve: log log log ab a b 6. Solve the following inequality: 7. Find the inverse of f. log log 8 f log 5 8. Find the eact value of the trigonometric function for 5 cot. 9. Find the values of the other five trigonometric functions of t from the given information: tan t and sint 0. 50. Sketch at least one period of the following graphs, and identify the amplitude, period, phase shift, reflection, and vertical shift. y0sin 5. Evaluate tan tan ytan cos 7 sin
c) e) cossin 8 sin sin d) sin sin 5. Find the length of the arc that subtends a central angle of in a circle of radius 6 cm. 5. Find the radius of the circle if the area of a sector with central angle 5 cm. rad is 5. A 0-ft ladder leans against a building so that the angle between the ground and the ladder is 60. How high does the ladder reach on the building? b 55. Find the eact value of cos tan, b 0 56. A 0-ft ladder casts a shadow that is 00 ft. long. What is the angle of elevation of the sun?. 57. Solve ABC, if possible C 6, c 0, b 5 A 00, B 80, c c) C 7, a 9, b. 58. Find the area of a triangle with side lengths: a 9, b, c 5