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

Subtract full rotations of ${\displaystyle 2\pi }$ until the angle is greater than or equal to ${\displaystyle 0}$ and less than ${\displaystyle 2\pi }$.

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.

The exact value of ${\displaystyle \sin \left(\frac{\pi }{2}\right)}$ is ${\displaystyle 1}$.

Multiply ${\displaystyle -1}$ by ${\displaystyle 1}$.

Raise ${\displaystyle -1}$ to the power of ${\displaystyle 2}$.

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.

The exact value of ${\displaystyle \tan \left(\frac{\pi }{4}\right)}$ is ${\displaystyle 1}$.

Multiply ${\displaystyle -1}$ by ${\displaystyle 1}$.

Multiply ${\displaystyle 3}$ by ${\displaystyle -1}$.