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# Y x 16 7 pts obtain the exact value of sin9 π 8 show

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y x 16. (7 pts) Obtain the exact value of sin(9 π /8). Show all the uses of appropriate identities and formulas. [Hints: Reference angle? Quadrant??] sin(9 π /8) =

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Final Exam/MAC1114 Page 5 of 8 17. (5 pts.) Find the exact value of sin -1 (sin(-7 π /5)). sin -1 (sin(-7 π /5)) = 18. (5 pts.) Write sin(cos -1 (u ) + sin -1 (v)) as an algebraic expression containing u and v. sin(cos -1 (u ) + sin -1 (v)) = 19. (5 pts.) Find the exact value of tan(2 tan -1 (3/4)). tan(2 tan -1 (3/4)) = 20. (5 pts.) Carefully sketch the graph ofy=c o s -1 (x). Label very carefully. y x 21. (5 pts.) Carefully sketch the graph ofy=t a n -1 (x).
Final Exam/MAC1114 Page 6 of 8 22. (10 pts.) Establish the following identity. 1 - cos( α ) sin( α ) = sin( α ) 1 + cos( α ) 23. (15 pts.) Very carefully complete the following derivation of a couple of half angle identities by giving the information requested and performing the computations needed. (a) Write down the trigonometric identity giving cos(x + y) in terms of sums of products of sines and cosines of x’s and y’s. cos(x + y) = (b) Uniformly replace each instance ofayb yxi nt h e identity above to obtain an identity for cos(2x). Use exponentiation to clean up the products appearing. cos(2x) = cos(x + x) = (c) Using the Pythagorean identity connecting sin 2 (x) and cos 2 (x), replace sin 2 (x) in the identity for cos(2x) and then

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y x 16 7 pts Obtain the exact value of sin9 π 8 Show all...

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