Geometry

Sum and Difference Trigonometric Formulas

Double Angle Identities

         

Given that sin2θ=13\sin^2 \theta = \frac{1}{3}, what is the value of 72cos(2θ)72 \cos(2 \theta)?

It is given that sin(θ)=137\sin(\theta) = \frac{1}{\sqrt{37}}. If cos(2θ)=ab \cos ( 2 \theta ) = \frac{a}{b} , where aa and bb are coprime positive integers, what is the value of a+ba+b?

xx is an angle measured in radians and satisfies π2<x<π2\frac{-\pi}{2} < x < \frac{\pi}{2}. It is given that sin(x)=817\sin(x) = \frac{8}{17}. If sin(2x)\sin(2x) can be written as ab\frac{a}{b}, where aa and bb are positive, coprime integers, what is the value of a+ba+b?

The double angle identity states that

cos(2θ)=Ncos2θM, \cos (2 \theta) = N \cos^2 \theta - M,

where NN and MM are real numbers. What is the value of N+M N + M ?

The double angle identity states that

sin(2θ)=Nsinθcosθ+M, \sin ( 2 \theta ) = N \sin \theta \cos \theta + M,

where NN and MM are real numbers. What is the value of N+MN + M ?

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