Trigonometry Examples

$(1, 0)$

Step 1

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

Opposite : $0$

Adjacent : $1$

Step 2

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

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Step 2.1

One to any power is one.

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

Step 2.2

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

$\sqrt{1 + 0}$

Step 2.3

Add $1$ and $0$ .

$\sqrt{1}$

Step 2.4

Any root of $1$ is $1$ .

$1$

Step 3

$\sin (θ) = \frac{Opposite}{Hypotenuse}$ therefore $\sin (θ) = \frac{0}{1}$ .

$\frac{0}{1}$

Step 4

Divide $0$ by $1$ .

$\sin (θ) = 0$