Trigonometry Examples

$(0, 2 p)$

Step 1

To find the $\sin (θ)$ between the x-axis and the line between the points $(0, 0)$ and $(0, 2 p)$ , draw the triangle between the three points $(0, 0)$ , $(0, 0)$ , and $(0, 2 p)$ .

Opposite : $2 p$

Adjacent : $0$

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

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

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

Step 2.1.2

Apply the product rule to $2 p$ .

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

Step 2.1.3

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

$\sqrt{0 + 4 p^{2}}$

Step 2.1.4

Add $0$ and $4 p^{2}$ .

$\sqrt{4 p^{2}}$

Step 2.2

Rewrite $4 p^{2}$ as ${(2 p)}^{2}$ .

$\sqrt{{(2 p)}^{2}}$

Step 2.3

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

$2 p$

Step 3

$\sin (θ) = \frac{Opposite}{Hypotenuse}$ therefore $\sin (θ) = \frac{2 p}{2 p}$ .

$\frac{2 p}{2 p}$

Step 4

Simplify $\sin (θ)$ .

Tap for more steps...

Step 4.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 4.1.1

Cancel the common factor.

$\sin (θ) = \frac{2 p}{2 p}$

Step 4.1.2

Rewrite the expression.

$\sin (θ) = \frac{p}{p}$

Step 4.2

Cancel the common factor of $p$ .

Tap for more steps...

Step 4.2.1

Cancel the common factor.

$\sin (θ) = \frac{p}{p}$

Step 4.2.2

Rewrite the expression.

$\sin (θ) = 1$