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Sum and Difference Trigonometric Formulas

These formulas explain how to add and subtract trigonometric functions (and their arguments). If you've got sum time, see what a difference these formulas will make for your trig toolkit.

Double Angle Identities

         

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

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

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

The double angle identity states that

\[ \cos (2 \theta) = N \cos^2 \theta - M, \]

where \(N\) and \(M\) are real numbers. What is the value of \( N + M \)?

The double angle identity states that

\[ \sin ( 2 \theta ) = N \sin \theta \cos \theta + M, \]

where \(N\) and \(M\) are real numbers. What is the value of \(N + M \)?

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