Trigonometry Examples

$A = \frac{1}{2} \cdot ((8) (12) \sin (135))$

Step 1

Remove parentheses.

$A = \frac{1}{2} \cdot (((8) (12)) \sin (135))$

Step 2

Remove parentheses.

$A = \frac{1}{2} \cdot 8 \cdot (12 \sin (135))$

Step 3

Simplify $\frac{1}{2} \cdot 8 \cdot (12 \sin (135))$ .

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Step 3.1

Cancel the common factor of $2$ .

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Step 3.1.1

Factor $2$ out of $8$ .

$A = \frac{1}{2} \cdot (2 (4)) \cdot (12 \sin (135))$

Step 3.1.2

Cancel the common factor.

$A = \frac{1}{2} \cdot (2 \cdot 4) \cdot (12 \sin (135))$

Step 3.1.3

Rewrite the expression.

$A = 4 \cdot (12 \sin (135))$

Step 3.2

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.

$A = 4 \cdot (12 \sin (45))$

Step 3.3

The exact value of $\sin (45)$ is $\frac{\sqrt{2}}{2}$ .

$A = 4 \cdot (12 \frac{\sqrt{2}}{2})$

Step 3.4

Cancel the common factor of $2$ .

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Step 3.4.1

Factor $2$ out of $12$ .

$A = 4 \cdot (2 (6) \frac{\sqrt{2}}{2})$

Step 3.4.2

Cancel the common factor.

$A = 4 \cdot (2 \cdot 6 \frac{\sqrt{2}}{2})$

Step 3.4.3

Rewrite the expression.

$A = 4 \cdot (6 \sqrt{2})$

Step 3.5

Multiply $6$ by $4$ .

$A = 24 \sqrt{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$A = 24 \sqrt{2}$

Decimal Form:

$A = 33.94112549 \dots$