Trigonometry Examples

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

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

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

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

Step 1

Identify the known sides of the triangle using

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

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

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

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

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

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

Step 3

Use

hyp = 13

$hyp = 13$ and

opp = 5

$opp = 5$ to find the value of the sine function.

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

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

Step 4

Use

hyp = 13

$hyp = 13$ and

adj = 12

$adj = 12$ to find the value of the cosine function.

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

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

Step 5

Use

opp = 5

$opp = 5$ and

adj = 12

$adj = 12$ to find the value of the tangent function.

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

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

Step 6

Use

opp = 5

$opp = 5$ and

adj = 12

$adj = 12$ to find the value of the cotangent function.

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

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

Step 7

The trig functions found are as follows:

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

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

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

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

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

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

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

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

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

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

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

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

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