Trigonometry Examples

$(- 5 a, - 12 a)$

Step 1

To find the $\sin (θ)$ between the x-axis and the line between the points $(0, 0)$ and $(- 5 a, - 12 a)$ , draw the triangle between the three points $(0, 0)$ , $(- 5 a, 0)$ , and $(- 5 a, - 12 a)$ .

Opposite : $- 12 a$

Adjacent : $- 5 a$

Step 2

Find the hypotenuse using Pythagorean theorem $c = \sqrt{a^{2} + b^{2}}$ .

Tap for more steps...

Step 2.1

Simplify the expression.

Tap for more steps...

Step 2.1.1

Apply the product rule to $- 5 a$ .

$\sqrt{{(- 5)}^{2} a^{2} + {(- 12 a)}^{2}}$

Step 2.1.2

Raise $- 5$ to the power of $2$ .

$\sqrt{25 a^{2} + {(- 12 a)}^{2}}$

Step 2.1.3

Apply the product rule to $- 12 a$ .

$\sqrt{25 a^{2} + {(- 12)}^{2} a^{2}}$

Step 2.1.4

Raise $- 12$ to the power of $2$ .

$\sqrt{25 a^{2} + 144 a^{2}}$

Step 2.2

Add $25 a^{2}$ and $144 a^{2}$ .

$\sqrt{169 a^{2}}$

Step 2.3

Rewrite $169 a^{2}$ as ${(13 a)}^{2}$ .

$\sqrt{{(13 a)}^{2}}$

Step 2.4

Pull terms out from under the radical, assuming positive real numbers.

$13 a$

Step 3

$\sin (θ) = \frac{Opposite}{Hypotenuse}$ therefore $\sin (θ) = \frac{- 12 a}{13 a}$ .

$\frac{- 12 a}{13 a}$

Step 4

Simplify $\sin (θ)$ .

Tap for more steps...

Step 4.1

Cancel the common factor of $a$ .

Tap for more steps...

Step 4.1.1

Cancel the common factor.

$\sin (θ) = \frac{- 12 a}{13 a}$

Step 4.1.2

Rewrite the expression.

$\sin (θ) = \frac{- 12}{13}$

Step 4.2

Move the negative in front of the fraction.

$\sin (θ) = - \frac{12}{13}$

Step 5

Approximate the result.

$\sin (θ) = - \frac{12}{13} \approx - 0.\overline{923076}$