Trigonometry Examples

(1, 0)

$(1, 0)$

Step 1

To find the

sin (θ)

$\sin (θ)$ between the x-axis and the line between the points

(0, 0)

$(0, 0)$ and

(1, 0)

$(1, 0)$ , draw the triangle between the three points

(0, 0)

$(0, 0)$ ,

(1, 0)

$(1, 0)$ , and

(1, 0)

$(1, 0)$ .

Opposite :

0

$0$

Adjacent :

1

$1$

Step 2

Find the hypotenuse using Pythagorean theorem

c = \sqrt{a^{2} + b^{2}}

$c = \sqrt{a^{2} + b^{2}}$ .

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Step 2.1

One to any power is one.

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

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

Step 2.2

Raising

0

$0$ to any positive power yields

0

$0$ .

\sqrt{1 + 0}

$\sqrt{1 + 0}$

Step 2.3

Add

1

$1$ and

0

$0$ .

\sqrt{1}

$\sqrt{1}$

Step 2.4

Any root of

1

$1$ is

1

$1$ .

1

$1$

1

$1$

Step 3

sin (θ) = \frac{Opposite}{Hypotenuse}

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

sin (θ) = \frac{0}{1}

$\sin (θ) = \frac{0}{1}$ .

\frac{0}{1}

$\frac{0}{1}$

Step 4

Divide

0

$0$ by

1

$1$ .

sin (θ) = 0

$\sin (θ) = 0$