Trigonometry Examples

$(24, - 7)$

Step 1

To find the $\sec (θ)$ between the x-axis and the line between the points $(0, 0)$ and $(24, - 7)$ , draw the triangle between the three points $(0, 0)$ , $(24, 0)$ , and $(24, - 7)$ .

Opposite : $- 7$

Adjacent : $24$

Step 2

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

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Step 2.1

Raise $24$ to the power of $2$ .

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

Step 2.2

Raise $- 7$ to the power of $2$ .

$\sqrt{576 + 49}$

Step 2.3

Add $576$ and $49$ .

$\sqrt{625}$

Step 2.4

Rewrite $625$ as $25^{2}$ .

$\sqrt{25^{2}}$

Step 2.5

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

$25$

Step 3

$\sec (θ) = \frac{Hypotenuse}{Adjacent}$ therefore $\sec (θ) = \frac{25}{24}$ .

$\frac{25}{24}$

Step 4

Approximate the result.

$\sec (θ) = \frac{25}{24} \approx 1.041\overline{6}$