Find the Exact Value sin((7pi)/2)^2+3tan((7pi)/4)

$\sin^{2} (\frac{7 π}{2}) + 3 \tan (\frac{7 π}{4})$

Simplify each term.

Subtract full rotations of $2 π$ until the angle is greater than or equal to $0$ and less than $2 π$ .

$\sin^{2} (\frac{3 π}{2}) + 3 \tan (\frac{7 π}{4})$

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

${(- \sin (\frac{π}{2}))}^{2} + 3 \tan (\frac{7 π}{4})$

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

${(- 1 \cdot 1)}^{2} + 3 \tan (\frac{7 π}{4})$

Multiply $- 1$ by $1$ .

${(- 1)}^{2} + 3 \tan (\frac{7 π}{4})$

Raise $- 1$ to the power of $2$ .

$1 + 3 \tan (\frac{7 π}{4})$

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.

$1 + 3 (- \tan (\frac{π}{4}))$

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

$1 + 3 (- 1 \cdot 1)$

Multiply $- 1$ by $1$ .

$1 + 3 \cdot - 1$

Multiply $3$ by $- 1$ .

$1 - 3$

Subtract $3$ from $1$ .

$- 2$

Find the Exact Value sin((7pi)/2)^2+3tan((7pi)/4)

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