Geometry

Trigonometric Equations

Trigonometric Equations - R method

         

In the interval [0,20π] [0, 20 \pi ] , how many solutions are there to

sinθ+cosθ=1? \sin \theta + \cos \theta = 1?

What is the maximum value of the function f(x)=2sin(x+π3)+3cosx+2?f(x)=2\sin \left(x+\frac{\pi}{3}\right)+\sqrt{3}\cos x+2 ?

The sum of all the θ\theta's in the interval 12π<θ<14π12\pi < \theta < 14\pi such that the quadratic equation for xx x22(sinθ+cosθ)x+cos2θ=0x^2-2(\sin \theta+\cos \theta)x+\cos 2\theta=0 has a repeated root is a2π\frac{a}{2}\pi. What is the value of a?a?

If provided that 3cosθ+sinθ=32\sqrt{3}\cos \theta+\sin \theta=\frac{\sqrt{3}}{2} and π2<θ<π,\displaystyle \frac{\pi}{2} < \theta < \pi, what is the value of 3sinθcosθ?\sqrt{3}\sin \theta-\cos \theta ?

What are the maximum and minimum values of the function y=2sinxcosx?y=\sqrt{2}\sin x-\cos x ?

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