Trigonometry Examples

$\sin (a) = \frac{4}{5}$

Step 1

Take the inverse sine of both sides of the equation to extract $a$ from inside the sine.

$a = \arcsin (\frac{4}{5})$

Step 2

Simplify the right side.

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Evaluate $\arcsin (\frac{4}{5})$ .

$a = 0.92729521$

Step 3

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

$a = (3.14159265) - 0.92729521$

Step 4

Solve for $a$ .

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Remove parentheses.

$a = 3.14159265 - 0.92729521$

Remove parentheses.

$a = (3.14159265) - 0.92729521$

Subtract $0.92729521$ from $3.14159265$ .

$a = 2.21429743$

Step 5

Find the period of $\sin (a)$ .

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The period of the function can be calculated using $\frac{2 π}{| b |}$ .

$\frac{2 π}{| b |}$

Replace $b$ with $1$ in the formula for period.

$\frac{2 π}{| 1 |}$

The absolute value is the distance between a number and zero. The distance between $0$ and $1$ is $1$ .

$\frac{2 π}{1}$

Divide $2 π$ by $1$ .

$2 π$

Step 6

The period of the $\sin (a)$ function is $2 π$ so values will repeat every $2 π$ radians in both directions.

$a = 0.92729521 + 2 π n, 2.21429743 + 2 π n$ , for any integer $n$