Trigonometry Examples

(24, - 7)

$(24, - 7)$

Step 1

To find the

\cos (θ)

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

(0, 0)

$(0, 0)$ and

(24, - 7)

$(24, - 7)$ , draw the triangle between the three points

(0, 0)

$(0, 0)$ ,

(24, 0)

$(24, 0)$ , and

(24, - 7)

$(24, - 7)$ .

Opposite :

- 7

$- 7$

Adjacent :

24

$24$

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

Raise

24

$24$ to the power of

2

$2$ .

\sqrt{576 + {(- 7)}^{2}}

$\sqrt{576 + {(- 7)}^{2}}$

Step 2.2

Raise

- 7

$- 7$ to the power of

2

$2$ .

\sqrt{576 + 49}

$\sqrt{576 + 49}$

Step 2.3

Add

576

$576$ and

49

$49$ .

\sqrt{625}

$\sqrt{625}$

Step 2.4

Rewrite

625

$625$ as

25^{2}

$25^{2}$ .

\sqrt{25^{2}}

$\sqrt{25^{2}}$

Step 2.5

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

25

$25$

25

$25$

Step 3

\cos (θ) = \frac{Adjacent}{Hypotenuse}

$\cos (θ) = \frac{Adjacent}{Hypotenuse}$ therefore

\cos (θ) = \frac{24}{25}

$\cos (θ) = \frac{24}{25}$ .

\frac{24}{25}

$\frac{24}{25}$

Step 4

Approximate the result.

\cos (θ) = \frac{24}{25} \approx 0.96

$\cos (θ) = \frac{24}{25} \approx 0.96$