Geometry

Trigonometric Equations

Trigonometric Equations - Factoring

         

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

6cos2θ10cosθ+3sin2θ=0? 6 \cos^2 \theta - 10 \cos \theta + 3 \sin^2 \theta = 0 ?

Which of the following are the solutions to the equation

6tan2θ17tanθ+2sec2θ=0? 6 \tan^2 \theta - 17 \tan \theta + 2 \sec^2 \theta = 0 ?

If 2πx<4π2\pi \leq x < 4\pi, the sum of all the xx's that satisfy tanx+1tanx2=0\tan x+ \frac{1}{\tan x}-2=0 can be expressed as aπa\pi. What is the value of 2a?2a?

The two roots of the quadratic equation 2x2x+k=02x^2-x+k=0 are sinθ\sin \theta and cosθ\cos \theta. What is 16(sin3θ+cos3θ)?16(\sin^3 \theta+\cos^3 \theta)?

In the domain [0,1000] [0^\circ , 1000^\circ ] , how many solutions are there to 4sin2θ3sinθ1=0 4 \sin^2 \theta - 3 \sin \theta - 1 = 0 ?

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