Find the Exact Value sin((5pi)/6)+2tan((7pi)/4)

$\sin (\frac{5 π}{6}) + 2 \tan (\frac{7 π}{4})$

Step 1

Simplify each term.

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

$\sin (\frac{π}{6}) + 2 \tan (\frac{7 π}{4})$

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

$\frac{1}{2} + 2 \tan (\frac{7 π}{4})$

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because tangent is negative in the fourth quadrant.

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

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

$\frac{1}{2} + 2 (- 1 \cdot 1)$

Multiply $2 (- 1 \cdot 1)$ .

Multiply $- 1$ by $1$ .

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

Multiply $2$ by $- 1$ .

$\frac{1}{2} - 2$

Step 2

To write $- 2$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{1}{2} - 2 \cdot \frac{2}{2}$

Step 3

Combine $- 2$ and $\frac{2}{2}$ .

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

Step 4

Combine the numerators over the common denominator.

$\frac{1 - 2 \cdot 2}{2}$

Step 5

Simplify the numerator.

Multiply $- 2$ by $2$ .

$\frac{1 - 4}{2}$

Subtract $4$ from $1$ .

$\frac{- 3}{2}$

Step 6

Move the negative in front of the fraction.

$- \frac{3}{2}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{3}{2}$

Decimal Form:

$- 1.5$

Mixed Number Form:

$- 1 \frac{1}{2}$

Find the Exact Value sin((5pi)/6)+2tan((7pi)/4)

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