Α 512 with π α 3 π 2 and sin β 12 with π β 3

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α ) = 5/12 with π < α < 3 π /2 and sin( β ) = -1/2 with π < β < 3 π /2. Show all the uses of appropriate identities. sin( α - β ) = cos( α + β ) =
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TEST-02/MAC1114 Page 3 of 4 7. (5 pts.) Obtain the exact value of sin( π /8). Show all the uses of appropriate identities. sin( π /8) = 8. (5 pts.) If sec( θ ) = 3 and sin( θ ) > 0, what is the exact value of cos(2 θ ) ?? Show all the uses of appropriate identities. cos(2 θ ) = 9. (5 pts.) Express the following product as a sum containing only sines or cosines. sin(4 θ )cos(6 θ ) = 10. (5 pts.) Use your calculator to find the value of sec -1 (-4/3) rounded to two decimal places. sec -1 (-4/3) = 11. (5 pts.) Find the exact value of sin -1 (sin(-7 π /6)). sin -1 (sin(-7 π /6)) = 12. (5 pts.) Write cos(cos -1 (u ) + sin -1 (v)) as an algebraic expression containing u and v. cos(cos -1 (u ) + sin -1 (v)) = 13. (5 pts.) Find the exact value of tan(2 tan -1 (3/4)). tan(2 tan -1 (3/4)) =
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TEST-02/MAC1114 Page 4 of 4 14. (5 pts.) Carefully sketch the graph of y = sin -1 (x). Label very carefully. y x 15. (5 pts.) Carefully sketch the graph of y = cos -1 (x). Label very carefully. y x 16. (5 pts.) Carefully sketch the graph of y = tan -1 (x). Label very carefully. y x
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