Trigonometry Examples

$\sin (x) - 1 = - 1$

Step 1

Move all terms not containing $\sin (x)$ to the right side of the equation.

Tap for more steps...

Step 1.1

Add $1$ to both sides of the equation.

$\sin (x) = - 1 + 1$

Step 1.2

Add $- 1$ and $1$ .

$\sin (x) = 0$

Step 2

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

$x = \arcsin (0)$

Step 3

Simplify the right side.

Tap for more steps...

Step 3.1

The exact value of $\arcsin (0)$ is $0$ .

$x = 0$

Step 4

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.

$x = π - 0$

Step 5

Subtract $0$ from $π$ .

$x = π$

Step 6

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

Tap for more steps...

Step 6.1

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

$\frac{2 π}{| b |}$

Step 6.2

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

$\frac{2 π}{| 1 |}$

Step 6.3

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

$\frac{2 π}{1}$

Step 6.4

Divide $2 π$ by $1$ .

$2 π$

Step 7

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

$x = 2 π n, π + 2 π n$ , for any integer $n$

Step 8

Consolidate the answers.

$x = π n$ , for any integer $n$