Trigonometry Examples

$\frac{\tan (\frac{π}{4})}{2} + \frac{1}{\csc (\frac{π}{6})}$

Step 1

Simplify each term.

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Step 1.1

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

$\frac{1}{2} + \frac{1}{\csc (\frac{π}{6})}$

Step 1.2

Rewrite $\csc (\frac{π}{6})$ in terms of sines and cosines.

$\frac{1}{2} + \frac{1}{\frac{1}{\sin (\frac{π}{6})}}$

Step 1.3

Multiply by the reciprocal of the fraction to divide by $\frac{1}{\sin (\frac{π}{6})}$ .

$\frac{1}{2} + 1 \sin (\frac{π}{6})$

Step 1.4

Multiply $\sin (\frac{π}{6})$ by $1$ .

$\frac{1}{2} + \sin (\frac{π}{6})$

Step 1.5

The exact value of $\sin (\frac{π}{6})$ is $\frac{1}{2}$ .

$\frac{1}{2} + \frac{1}{2}$

Step 2

Combine fractions.

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Step 2.1

Combine the numerators over the common denominator.

$\frac{1 + 1}{2}$

Step 2.2

Simplify the expression.

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Step 2.2.1

Add $1$ and $1$ .

$\frac{2}{2}$

Step 2.2.2

Divide $2$ by $2$ .

$1$