Geometry

Trigonometric Equations

Trigonometric Equations - Double Angle Formula

         

In the domain [0,1000] [0^\circ , 1000^\circ ] , how many solutions are there to sinθcosθ=12 \sin \theta \cos \theta = \frac {1} {2} ?

In the interval [0,2π] [0, 2 \pi ] , how many solutions are there to

sinθ=2sin2θ? \sin \theta = 2 \sin 2 \theta ?

How many xx's in the interval 0x29π0 \leq x \leq 29\pi satisfy sin(2xπ5)=sinπ8?\sin \left(2x-\frac{\pi}{5}\right)=\sin \frac{\pi}{8}?

How many xx's in the interval 0x60π0 \leq x \leq 60\pi satisfy 6cos2x+23sinx4=0?6\cos 2x+23\sin x-4=0?

In the interval [0,2π] [0, 2 \pi ] , how many solutions are there to

cos2θ=cos2θ? \cos^2 \theta = \cos 2 \theta ?

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