Trigonometry Examples

$\sin^{2} (θ) - 4 (\cos (- θ) - 1) = 0$

Step 1

Simplify each term.

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Step 1.1

Since $\cos (- θ)$ is an even function, rewrite $\cos (- θ)$ as $\cos (θ)$ .

$\sin^{2} (θ) - 4 (\cos (θ) - 1) = 0$

Step 1.2

Apply the distributive property.

$\sin^{2} (θ) - 4 \cos (θ) - 4 \cdot - 1 = 0$

Step 1.3

Multiply $- 4$ by $- 1$ .

$\sin^{2} (θ) - 4 \cos (θ) + 4 = 0$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$θ = 2 π n$ , for any integer $n$

Step 3