Trigonometry Examples

$2 \sin (3) θ \cos (3) θ$

Step 1

Simplify the expression.

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Step 1.1

Reorder $2 \sin (3) θ$ and $\cos (3)$ .

$\cos (3) (2 \sin (3) θ) θ$

Step 1.2

Move parentheses.

$\cos (3) (2 \sin (3)) θ \cdot θ$

Step 1.3

Reorder $\cos (3)$ and $2 \sin (3)$ .

$2 \sin (3) \cos (3) θ \cdot θ$

$2 \sin (3) \cos (3) θ \cdot θ$

Step 2

Apply the sine double-angle identity.

$\sin (2 \cdot 3) θ \cdot θ$

Step 3

Multiply $θ$ by $θ$ by adding the exponents.

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Step 3.1

Move $θ$ .

$\sin (2 \cdot 3) (θ \cdot θ)$

Step 3.2

Multiply $θ$ by $θ$ .

$\sin (2 \cdot 3) θ^{2}$

$\sin (2 \cdot 3) θ^{2}$

Step 4

Multiply $2$ by $3$ .

$\sin (6) θ^{2}$

Step 5

Reorder factors in $\sin (6) θ^{2}$ .

$θ^{2} \sin (6)$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$