Trigonometry Examples

$\frac{1}{2} \cdot 40 \cdot 52 \cdot \sin (135)$

Step 1

Cancel the common factor of $2$ .

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Step 1.1

Factor $2$ out of $40$ .

$\frac{1}{2} \cdot (2 (20)) \cdot 52 \cdot \sin (135)$

Step 1.2

Cancel the common factor.

$\frac{1}{2} \cdot (2 \cdot 20) \cdot 52 \cdot \sin (135)$

Step 1.3

Rewrite the expression.

$20 \cdot 52 \cdot \sin (135)$

Step 2

Multiply $20$ by $52$ .

$1040 \cdot \sin (135)$

Step 3

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

$1040 \cdot \sin (45)$

Step 4

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

$1040 \cdot \frac{\sqrt{2}}{2}$

Step 5

Cancel the common factor of $2$ .

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Step 5.1

Factor $2$ out of $1040$ .

$2 (520) \cdot \frac{\sqrt{2}}{2}$

Step 5.2

Cancel the common factor.

$2 \cdot 520 \cdot \frac{\sqrt{2}}{2}$

Step 5.3

Rewrite the expression.

$520 \cdot \sqrt{2}$

$520 \sqrt{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$520 \sqrt{2}$

Decimal Form:

$735.39105243 \dots$