Geometry
Fundamental Trigonometric Identities
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?