Trigonometry Examples

$\tan (\frac{5 π}{4})$

Step 1

The angle $\frac{5 π}{4}$ is an angle where the values of the six trigonometric functions are known. Because this is the case, add $0$ to keep the value the same.

$\tan (\frac{5 π}{4} + 0)$

Step 2

Use the sum formula for tangent to simplify the expression. The formula states that $\tan (A + B) = \frac{\tan (A) + \tan (B)}{1 - \tan (A) \tan (B)}$ .

$\frac{\tan (\frac{5 π}{4}) + \tan (0)}{1 - \tan (\frac{5 π}{4}) \tan (0)}$

Step 3

Simplify the numerator.

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Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.

$\frac{\tan (\frac{π}{4}) + \tan (0)}{1 - \tan (\frac{5 π}{4}) \tan (0)}$

The exact value of $\tan (\frac{π}{4})$ is $1$ .

$\frac{1 + \tan (0)}{1 - \tan (\frac{5 π}{4}) \tan (0)}$

The exact value of $\tan (0)$ is $0$ .

$\frac{1 + 0}{1 - \tan (\frac{5 π}{4}) \tan (0)}$

Add $1$ and $0$ .

$\frac{1}{1 - \tan (\frac{5 π}{4}) \tan (0)}$

Step 4

Simplify the denominator.

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Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.

$\frac{1}{1 - \tan (\frac{π}{4}) \tan (0)}$

The exact value of $\tan (\frac{π}{4})$ is $1$ .

$\frac{1}{1 - 1 \cdot 1 \tan (0)}$

Multiply $- 1$ by $1$ .

$\frac{1}{1 - 1 \tan (0)}$

The exact value of $\tan (0)$ is $0$ .

$\frac{1}{1 - 1 \cdot 0}$

Multiply $- 1$ by $0$ .

$\frac{1}{1 + 0}$

Add $1$ and $0$ .

$\frac{1}{1}$

Step 5

Cancel the common factor of $1$ .

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Cancel the common factor.

$\frac{1}{1}$

Rewrite the expression.

$1$