Unformatted text preview: Verify the identity 2 csc(2 θ ) = sec( θ ) csc( θ ). 7. Verify the identity sin(3 θ )sin( θ ) = 2 cos(2 θ ) sin( θ ). 8. Sketch y = 2 sin( x ). 9. Sketch y = sin(3 x ). 10. Sketch y = sin(x ). 11. Find all of the solutions of 2 sin( t )1sin 2 ( t ) = 0 in the interval [0 , 2 π ]. ⇒ 4.2 The Derivative of sin x What about the derivative of the sine function? The rules for derivatives that we have are of no help, since sin x is not an algebraic function. We need to return to the deﬁnition of the derivative, set up a limit, and try to compute it. Here’s the deﬁnition: d dx sin x = lim Δ x → sin( x + Δ x )sin x Δ x . Using some trigonometric identies, we can make a little progress on the quotient: sin( x + Δ x )sin x Δ x = sin x cos Δ x + sin Δ x cos xsin x Δ x = sin x cos Δ x1 Δ x + cos x sin Δ x Δ x ....
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 Fall '07
 JonathanRogawski
 Math, Calculus, Trigonometry, Unit Circle, .........

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