Fundamental Trigonometric Identities

Trigonometric R method


Which of the following is equal to 4sinx+4cosx?4\sin x+4\cos x?

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

(18sinθ+3cosθ)2? (18 \sin \theta + 3 \cos \theta ) ^2 ?

What are the maximum and minimum values of 16sinx+163cosx?-16\sin x+16\sqrt{3}\cos x?

In the interval [0,4π],[0,4\pi], find the sum of all the solutions to the equation 26sin(x+π5)22cos(x+π5)=26.2\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 15sinx+8cosx, 15\sin x +8\cos x, where xx is a real number?


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