Evaluate Using the Given Value cos(theta) if tan(theta)=3/2

Take the inverse tangent of both sides of the equation to extract ${\displaystyle \theta }$ from inside the tangent.

The tangent function is positive in the first and third quadrants. To find the second solution, add the reference angle from ${\displaystyle \pi }$ to find the solution in the fourth quadrant.

The period of the ${\displaystyle \tan \left(\theta \right)}$ function is ${\displaystyle \pi }$ so values will repeat every ${\displaystyle \pi }$ radians in both directions.

${\displaystyle \theta =0.98279372+\pi n,4.12438637+\pi n}$, for any integer ${\displaystyle n}$

Consolidate ${\displaystyle 0.98279372+\pi n}$ and ${\displaystyle 4.12438637+\pi n}$ to ${\displaystyle 0.98279372+\pi n}$.

${\displaystyle \theta =0.98279372+\pi n}$, for any integer ${\displaystyle n}$

Take the base solution.

Replace the variable ${\displaystyle \theta }$ with ${\displaystyle 0.98279372}$ in the expression.