Unformatted text preview: 7 π 5 . 7. Suppose cos θ = 2 3 and 3 π 2 < θ < 2 π, ﬁnd the other ﬁve trigonometric functions of θ. 8. (a) Find all values of θ ∈ [0 , 2 π ) such that sin 2 θ = cos θ. (b) On the interval [0 , 2 π ] sketch the graph of y = cos 2 x. 9. Let θ = 0 , π 6 , π 4 , π 3 , π 2 ,π, 3 π 2 , 2 π. (a) Find the exact values for all six trigonometric functions of θ. (b) For any θ, state all pythagorean identities, double and halfangle identities, and sum formulas. 10. (a) Compute tan1 (1) , sin1 ( 1 2 ) , cos1 ( √ 3 2 ) , cos1 (0) . (b) Prove for any θ the identity: cos 3 θ = 4 cos 3 θ3 cos θ. 11. Rewrite as a function of x the expression: log 3 y = 2 + 4 log 3 (2 x ) 12. Let f ( x ) = x 2 for 0 6 x 6 1 . Find L n ,R n ,M n and show that lim n→∞ R n = 1 3 ....
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 Fall '08
 Staff
 Trigonometry, Euler's formula, Radian, Grad

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