Trigonometry Examples

$(p, 0)$

Step 1

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

Opposite : $0$

Adjacent : $p$

Step 2

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

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Step 2.1

Raising $0$ to any positive power yields $0$ .

$\sqrt{p^{2} + 0}$

Step 2.2

Add $p^{2}$ and $0$ .

$\sqrt{p^{2}}$

Step 2.3

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

$p$

Step 3

$\sin (θ) = \frac{Opposite}{Hypotenuse}$ therefore $\sin (θ) = \frac{0}{p}$ .

$\frac{0}{p}$

Step 4

Divide $0$ by $p$ .

$\sin (θ) = 0$