Trigonometry Examples

$\csc (x) = \frac{5}{3}$ , $\tan (x) = \frac{3}{4}$

Step 1

Identify the known sides of the triangle using $\csc (x) = \frac{5}{3}$ .

$\csc (x) = \frac{1}{\sin (x)} = \frac{hyp}{opp} = \frac{5}{3}$

Step 2

Identify the known sides of the triangle using $\tan (x) = \frac{3}{4}$ .

$\tan (x) = \frac{opp}{adj} = \frac{3}{4}$

Step 3

Use $hyp = 5$ and $opp = 3$ to find the value of the sine function.

$\sin (x) = \frac{opp}{hyp} = \frac{3}{4}$

Step 4

Use $hyp = 5$ and $adj = 4$ to find the value of the cosine function.

$\cos (x) = \frac{adj}{hyp} = \frac{4}{5}$

Step 5

Use $hyp = 5$ and $adj = 4$ to find the value of the secant function.

$\sec (x) = \frac{1}{\cos (x)} = \frac{hyp}{adj} = \frac{5}{4}$

Step 6

Use $opp = 3$ and $adj = 4$ to find the value of the cotangent function.

$\cot (x) = \frac{1}{\tan (x)} = \frac{adj}{opp} = \frac{4}{3}$

Step 7

The trig functions found are as follows:

$\sin (x) = \frac{3}{4}$

$\cos (x) = \frac{4}{5}$

$\tan (x) = \frac{3}{4}$

$\cot (x) = \frac{4}{3}$

$\sec (x) = \frac{5}{4}$

$\csc (x) = \frac{5}{3}$

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