Trigonometry Examples

$\arcsin (\frac{1240 (\sin (135))}{2570.9})$

Step 1

Simplify the numerator.

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Step 1.1

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

$\arcsin (\frac{1240 \sin (45)}{2570.9})$

Step 1.2

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

$\arcsin (\frac{1240 \frac{\sqrt{2}}{2}}{2570.9})$

Step 2

Combine $1240$ and $\frac{\sqrt{2}}{2}$ .

$\arcsin (\frac{\frac{1240 \sqrt{2}}{2}}{2570.9})$

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Reduce the expression $\frac{1240 \sqrt{2}}{2}$ by cancelling the common factors.

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Step 3.1.1

Factor $2$ out of $1240 \sqrt{2}$ .

$\arcsin (\frac{\frac{2 (620 \sqrt{2})}{2}}{2570.9})$

Step 3.1.2

Factor $2$ out of $2$ .

$\arcsin (\frac{\frac{2 (620 \sqrt{2})}{2 (1)}}{2570.9})$

Step 3.1.3

Cancel the common factor.

$\arcsin (\frac{\frac{2 (620 \sqrt{2})}{2 \cdot 1}}{2570.9})$

Step 3.1.4

Rewrite the expression.

$\arcsin (\frac{\frac{620 \sqrt{2}}{1}}{2570.9})$

Step 3.2

Divide $620 \sqrt{2}$ by $1$ .

$\arcsin (\frac{620 \sqrt{2}}{2570.9})$

Step 4

Evaluate the root.

$\arcsin (\frac{620 \cdot 1.41421356}{2570.9})$

Step 5

Multiply $620$ by $1.41421356$ .

$\arcsin (\frac{876.81240867}{2570.9})$

Step 6

Divide $876.81240867$ by $2570.9$ .

$\arcsin (0.3410527)$

Step 7

Evaluate $\arcsin (0.3410527)$ .

$19.94102374$