Trigonometry Examples

$\sin (x) = \frac{7}{25}$ , $\cos (x) = \frac{24}{25}$

Step 1

To find the value of $\tan (x)$ , use the fact that $\tan (x) = \frac{\sin (x)}{\cos (x)}$ then substitute in the known values.

$\tan (x) = \frac{\sin (x)}{\cos (x)} = \frac{\frac{7}{25}}{\frac{24}{25}}$

Step 2

Simplify the result.

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Step 2.1

Multiply the numerator by the reciprocal of the denominator.

$\tan (x) = \frac{\sin (x)}{\cos (x)} = \frac{7}{25} \cdot \frac{25}{24}$

Step 2.2

Cancel the common factor of $25$ .

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Step 2.2.1

Cancel the common factor.

$\tan (x) = \frac{\sin (x)}{\cos (x)} = \frac{7}{25} \cdot \frac{25}{24}$

Step 2.2.2

Rewrite the expression.

$\tan (x) = \frac{\sin (x)}{\cos (x)} = 7 (\frac{1}{24})$

Step 2.3

Combine $7$ and $\frac{1}{24}$ .

$\tan (x) = \frac{\sin (x)}{\cos (x)} = \frac{7}{24}$

Step 3

To find the value of $\cot (x)$ , use the fact that $\frac{1}{\tan (x)}$ then substitute in the known values.

$\cot (x) = \frac{1}{\tan (x)} = \frac{1}{\frac{7}{24}}$

Step 4

Simplify the result.

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Step 4.1

Multiply the numerator by the reciprocal of the denominator.

$\cot (x) = \frac{1}{\tan (x)} = 1 (\frac{24}{7})$

Step 4.2

Multiply $\frac{24}{7}$ by $1$ .

$\cot (x) = \frac{1}{\tan (x)} = \frac{24}{7}$

Step 5

To find the value of $\sec (x)$ , use the fact that $\frac{1}{\cos (x)}$ then substitute in the known values.

$\sec (x) = \frac{1}{\cos (x)} = \frac{1}{\frac{24}{25}}$

Step 6

Simplify the result.

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Step 6.1

Multiply the numerator by the reciprocal of the denominator.

$\sec (x) = \frac{1}{\cos (x)} = 1 (\frac{25}{24})$

Step 6.2

Multiply $\frac{25}{24}$ by $1$ .

$\sec (x) = \frac{1}{\cos (x)} = \frac{25}{24}$

Step 7

To find the value of $\csc (x)$ , use the fact that $\frac{1}{\sin (x)}$ then substitute in the known values.

$\csc (x) = \frac{1}{\sin (x)} = \frac{1}{\frac{7}{25}}$

Step 8

Simplify the result.

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Step 8.1

Multiply the numerator by the reciprocal of the denominator.

$\csc (x) = \frac{1}{\sin (x)} = 1 (\frac{25}{7})$

Step 8.2

Multiply $\frac{25}{7}$ by $1$ .

$\csc (x) = \frac{1}{\sin (x)} = \frac{25}{7}$

Step 9

The trig functions found are as follows:

$\sin (x) = \frac{7}{25}$

$\cos (x) = \frac{24}{25}$

$\tan (x) = \frac{7}{24}$

$\cot (x) = \frac{24}{7}$

$\sec (x) = \frac{25}{24}$

$\csc (x) = \frac{25}{7}$