Trigonometry Examples

(21, 28)

$(21, 28)$

Step 1

To find the

\sin (θ)

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

(0, 0)

$(0, 0)$ and

(21, 28)

$(21, 28)$ , draw the triangle between the three points

(0, 0)

$(0, 0)$ ,

(21, 0)

$(21, 0)$ , and

(21, 28)

$(21, 28)$ .

Opposite :

28

$28$

Adjacent :

21

$21$

Step 2

Find the hypotenuse using Pythagorean theorem

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

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

Tap for more steps...

Step 2.1

Raise

21

$21$ to the power of

2

$2$ .

\sqrt{441 + {(28)}^{2}}

$\sqrt{441 + {(28)}^{2}}$

Step 2.2

Raise

28

$28$ to the power of

2

$2$ .

\sqrt{441 + 784}

$\sqrt{441 + 784}$

Step 2.3

Add

441

$441$ and

784

$784$ .

\sqrt{1225}

$\sqrt{1225}$

Step 2.4

Rewrite

1225

$1225$ as

35^{2}

$35^{2}$ .

\sqrt{35^{2}}

$\sqrt{35^{2}}$

Step 2.5

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

35

$35$

35

$35$

Step 3

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

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

\sin (θ) = \frac{28}{35}

$\sin (θ) = \frac{28}{35}$ .

\frac{28}{35}

$\frac{28}{35}$

Step 4

Cancel the common factor of

28

$28$ and

35

$35$ .

Tap for more steps...

Step 4.1

Factor

7

$7$ out of

28

$28$ .

\sin (θ) = \frac{7 (4)}{35}

$\sin (θ) = \frac{7 (4)}{35}$

Step 4.2

Cancel the common factors.

Tap for more steps...

Step 4.2.1

Factor

7

$7$ out of

35

$35$ .

\sin (θ) = \frac{7 \cdot 4}{7 \cdot 5}

$\sin (θ) = \frac{7 \cdot 4}{7 \cdot 5}$

Step 4.2.2

Cancel the common factor.

\sin (θ) = \frac{7 \cdot 4}{7 \cdot 5}

$\sin (θ) = \frac{7 \cdot 4}{7 \cdot 5}$

Step 4.2.3

Rewrite the expression.

\sin (θ) = \frac{4}{5}

$\sin (θ) = \frac{4}{5}$

\sin (θ) = \frac{4}{5}

$\sin (θ) = \frac{4}{5}$

\sin (θ) = \frac{4}{5}

$\sin (θ) = \frac{4}{5}$

Step 5

Approximate the result.

\sin (θ) = \frac{4}{5} \approx 0.8

$\sin (θ) = \frac{4}{5} \approx 0.8$