Trigonometry Examples

$0 = (\frac{1}{12}) (\sqrt{3} \cos (8 t) - 3 \sin (8 t))$

Step 1

Simplify $(\frac{1}{12}) (\sqrt{3} \cos (8 t) - 3 \sin (8 t))$ .

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Step 1.1

Apply the distributive property.

$0 = \frac{1}{12} (\sqrt{3} \cos (8 t)) + \frac{1}{12} (- 3 \sin (8 t))$

Step 1.2

Multiply $\frac{1}{12} (\sqrt{3} \cos (8 t))$ .

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Step 1.2.1

Combine $\sqrt{3}$ and $\frac{1}{12}$ .

$0 = \frac{\sqrt{3}}{12} \cos (8 t) + \frac{1}{12} (- 3 \sin (8 t))$

Step 1.2.2

Combine $\frac{\sqrt{3}}{12}$ and $\cos (8 t)$ .

$0 = \frac{\sqrt{3} \cos (8 t)}{12} + \frac{1}{12} (- 3 \sin (8 t))$

Step 1.3

Cancel the common factor of $3$ .

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Step 1.3.1

Factor $3$ out of $12$ .

$0 = \frac{\sqrt{3} \cos (8 t)}{12} + \frac{1}{3 (4)} (- 3 \sin (8 t))$

Step 1.3.2

Factor $3$ out of $- 3 \sin (8 t)$ .

$0 = \frac{\sqrt{3} \cos (8 t)}{12} + \frac{1}{3 (4)} (3 (- \sin (8 t)))$

Step 1.3.3

Cancel the common factor.

$0 = \frac{\sqrt{3} \cos (8 t)}{12} + \frac{1}{3 \cdot 4} (3 (- \sin (8 t)))$

Step 1.3.4

Rewrite the expression.

$0 = \frac{\sqrt{3} \cos (8 t)}{12} + \frac{1}{4} (- \sin (8 t))$

Step 1.4

Combine $\frac{1}{4}$ and $\sin (8 t)$ .

$0 = \frac{\sqrt{3} \cos (8 t)}{12} - \frac{\sin (8 t)}{4}$

Step 2

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

$t \approx 0.06544984 + \frac{π n}{8}$ , for any integer $n$

Step 3