Precalculus Examples

$\sin (20) \cdot 56 = \sin (118) a$

Step 1

Rewrite the equation as $\sin (118) a = \sin (20) \cdot 56$ .

$\sin (118) a = \sin (20) \cdot 56$

Step 2

For the two functions to be equal, the arguments of each must be equal.

$118 = 20$

Step 3

Since $118 \neq 20$ , there are no solutions.

No solution

Step 4

The sine function is positive in the first and second quadrants. To find the second solution, subtract the reference angle from $180$ to find the solution in the second quadrant.

$118 = 180 - 20$

Step 5

Solve for $a$ .

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Step 5.1

Subtract $20$ from $180$ .

$118 = 160$

Step 5.2

Since $118 \neq 160$ , there are no solutions.

No solution