Trigonometry Examples

$\sec (x) = \frac{13}{12}$ , $\csc (x) = \frac{13}{5}$

Step 1

Identify the known sides of the triangle using $\sec (x) = \frac{13}{12}$ .

$\sec (x) = \frac{1}{\cos (x)} = \frac{hyp}{adj} = \frac{13}{12}$

Step 2

Identify the known sides of the triangle using $\csc (x) = \frac{13}{5}$ .

$\csc (x) = \frac{1}{\sin (x)} = \frac{hyp}{opp} = \frac{13}{5}$

Step 3

Use $hyp = 13$ and $opp = 5$ to find the value of the sine function.

$\sin (x) = \frac{opp}{hyp} = \frac{5}{12}$

Step 4

Use $hyp = 13$ and $adj = 12$ to find the value of the cosine function.

$\cos (x) = \frac{adj}{hyp} = \frac{12}{13}$

Step 5

Use $opp = 5$ and $adj = 12$ to find the value of the tangent function.

$\tan (x) = \frac{opp}{adj} = \frac{5}{12}$

Step 6

Use $opp = 5$ and $adj = 12$ to find the value of the cotangent function.

$\cot (x) = \frac{1}{\tan (x)} = \frac{adj}{opp} = \frac{12}{5}$

Step 7

The trig functions found are as follows:

$\sin (x) = \frac{5}{12}$

$\cos (x) = \frac{12}{13}$

$\tan (x) = \frac{5}{12}$

$\cot (x) = \frac{12}{5}$

$\sec (x) = \frac{13}{12}$

$\csc (x) = \frac{13}{5}$