Question

find the angle of least positive measure (not equal to the given measure) that is coterminal with the angle 4398°. the measure is °. (simplify your answer.)

Explanation:

Step1: Recall coterminal - angle formula

Coterminal angles differ by a multiple of $360^{\circ}$. Let $\theta = 4398^{\circ}$ and we want to find $\alpha=\theta - n\times360^{\circ}$, where $n$ is an integer and $\alpha>0$.

Step2: Divide the given angle by 360

Divide $4398$ by $360$: $4398\div360 = 12\frac{78}{360}=12+\frac{13}{60}$.

Step3: Determine the value of n

We want to find the largest non - negative integer $n$ such that $\theta - n\times360^{\circ}>0$. When $n = 12$, $\alpha=4398 - 12\times360$.

Step4: Calculate the coterminal angle

$4398-12\times360=4398 - 4320=78^{\circ}$.

Answer:

$78$