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Fundamental Trigonometric Identities

Trigonometric 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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