Trigonometric Equations - Factoring Practice Problems Online

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

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

Which of the following are the solutions to the equation

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

\cot \theta = 2, \frac{1}{8}

\cot \theta = \frac{1}{2} , 8

\cot \theta = \frac{1}{2} , \frac{1}{ 8}

\cot \theta = 2 , 8

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

The two roots of the quadratic equation $2x^2-x+k=0$ are $\sin \theta$ and $\cos \theta$ . What is $16(\罪^ 3 \ theta+\cos^3 \theta)?$

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

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Trigonometric Equations - Factoring