Trigonometry Examples

$\sin^{2} (θ) - 16 = 0$

Step 1

Add $16$ to both sides of the equation.

$\sin^{2} (θ) = 16$

Step 2

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$\sin (θ) = \pm \sqrt{16}$

Step 3

Simplify $\pm \sqrt{16}$ .

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Step 3.1

Rewrite $16$ as $4^{2}$ .

$\sin (θ) = \pm \sqrt{4^{2}}$

Step 3.2

Pull terms out from under the radical, assuming positive real numbers.

$\sin (θ) = \pm 4$

Step 4

The complete solution is the result of both the positive and negative portions of the solution.

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Step 4.1

First, use the positive value of the $\pm$ to find the first solution.

$\sin (θ) = 4$

Step 4.2

Next, use the negative value of the $\pm$ to find the second solution.

$\sin (θ) = - 4$

Step 4.3

The complete solution is the result of both the positive and negative portions of the solution.

$\sin (θ) = 4, - 4$

Step 5

Set up each of the solutions to solve for $θ$ .

$\sin (θ) = 4$

$\sin (θ) = - 4$

Step 6

Solve for $θ$ in $\sin (θ) = 4$ .

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Step 6.1

The range of sine is $- 1 \leq y \leq 1$ . Since $4$ does not fall in this range, there is no solution.

No solution

Step 7

Solve for $θ$ in $\sin (θ) = - 4$ .

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Step 7.1

The range of sine is $- 1 \leq y \leq 1$ . Since $- 4$ does not fall in this range, there is no solution.

No solution