Trigonometry Examples

$(0, 1)$

Step 1

To find the $\sin (θ)$ between the x-axis and the line between the points $(0, 0)$ and $(0, 1)$ , draw the triangle between the three points $(0, 0)$ , $(0, 0)$ , and $(0, 1)$ .

Opposite : $1$

Adjacent : $0$

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 $0$ .

$\sqrt{0 + {(1)}^{2}}$

Step 2.2

One to any power is one.

$\sqrt{0 + 1}$

Step 2.3

Add $0$ and $1$ .

$\sqrt{1}$

Step 2.4

Any root of $1$ is $1$ .

$1$

Step 3

$\sin (θ) = \frac{Opposite}{Hypotenuse}$ therefore $\sin (θ) = \frac{1}{1}$ .

$\frac{1}{1}$

Step 4

Divide $1$ by $1$ .

$\sin (θ) = 1$