Trigonometry Examples

$(- 7, 24)$

Step 1

To find the $\sin (θ)$ between the x-axis and the line between the points $(0, 0)$ and $(- 7, 24)$ , draw the triangle between the three points $(0, 0)$ , $(- 7, 0)$ , and $(- 7, 24)$ .

Opposite : $24$

Adjacent : $- 7$

Step 2

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

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Step 2.1

Raise $- 7$ to the power of $2$ .

$\sqrt{49 + {(24)}^{2}}$

Step 2.2

Raise $24$ to the power of $2$ .

$\sqrt{49 + 576}$

Step 2.3

Add $49$ and $576$ .

$\sqrt{625}$

Step 2.4

Rewrite $625$ as $25^{2}$ .

$\sqrt{25^{2}}$

Step 2.5

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

$25$

Step 3

$\sin (θ) = \frac{Opposite}{Hypotenuse}$ therefore $\sin (θ) = \frac{24}{25}$ .

$\frac{24}{25}$

Step 4

Approximate the result.

$\sin (θ) = \frac{24}{25} \approx 0.96$