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Fundamental Trigonometric Identities

These are your basic building blocks for solving trigonometric equations and understanding how the pieces fit together. Using these identities can make sense of even the scariest looking trig.

R Method

         

Which of the following is equal to \(4\sin x+4\cos x?\)

As \(\theta\) ranges over all real values, what is the maximum value of

\[ (18 \sin \theta + 3 \cos \theta ) ^2 ? \]

What are the maximum and minimum values of \(-16\sin x+16\sqrt{3}\cos x?\)

In the interval \([0,4\pi],\) find the sum of all the solutions to the equation \[-2\sqrt{6}\sin\left(x+\frac{\pi}{5}\right)+2\sqrt{2}\cos\left(x+\frac{\pi}{5}\right)=2\sqrt{6}.\]

What is the largest possible value of \( 15\sin x +8\cos x,\) where \(x\) is a real number?

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