Trigonometry Examples

$c^{2} = 89 - 80 \cos (60)$

Step 1

Simplify $89 - 80 \cos (60)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

The exact value of $\cos (60)$ is $\frac{1}{2}$ .

$c^{2} = 89 - 80 (\frac{1}{2})$

Step 1.1.2

Cancel the common factor of $2$ .

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Step 1.1.2.1

Factor $2$ out of $- 80$ .

$c^{2} = 89 + 2 (- 40) \frac{1}{2}$

Step 1.1.2.2

Cancel the common factor.

$c^{2} = 89 + 2 \cdot - 40 \frac{1}{2}$

Step 1.1.2.3

Rewrite the expression.

$c^{2} = 89 - 40$

Step 1.2

Subtract $40$ from $89$ .

$c^{2} = 49$

Step 2

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

$c \approx - 12.85274439, 12.85274439$

Step 3