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Answer to: Rewrite the expression in terms of the functions cosx and sinx. csc x+tan^2xcsc x (a) 1/sinxcosx (b) sinx+cosx/sinxcosx (c) cosx-sinx...
Using the product-to-sum formula again for sinxsin3x:sinxsin3x=12(cos(2x)−cos(4x))Now we can substitute this back:12∫(1−cos(6x)2−12(cos(2x)−cos(4x)))dx Step 6: Combine and IntegrateCombining the terms gives:14∫(1−cos(6x)−cos(2x)+cos(4x))dxNow we can ...
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In the study of calculus, when we are asked to differentiate a function of a function, or a composition of functions, we have a special rule called the chain rule that we can use to do so. This rule states that the derivative of f(g(x)) is f ' (g(x)) ⋅ g ' (x)....
Given sinx = -1/3, and that the angle x is in the third quadrant, find sin2x and cos2x. Trigonometric Identities: The standard angle addition formulas for sine and cosine are given as sin(a+b)=sinacosb+cosasinbandcos(a+b)=cosacos...
And also know the formula, (a+b)2=a2+b2+2ab And a trigonometric form, 2sinx cosx=sin2xsin2x+cos2x=1 Answer and Explanation: We have, {eq}\displaystyle \begin{align*} \int \frac {\cos 2x \ dx}{(\sin x + \cos x)^2} &= \int \frac {...
Find the curvature in terms of t for r(t) = e^t\cos t\,i+ e^t \sin t\, j a. \displaystyle \frac{e^{-t{\sqrt{2 b. \displaystyle \frac{e^{-t{2} Use this formula to find the curvature. y = 3x^4 \kappa(x) = Find the curvature of the curve r(t) = \sin t i ...
\cos^{2x} = 2 + 2 \sin x Write your answer in radians in terms of' \pi. The equation cos x = x has a solution in what interval? Solve the trigonometric equation (cos x)(2cos x + 1) = 0 in the interval [0,360). Solve the trigonometric equation (\cos x)(...