QuestionFind the smallest positive angle (in degrees) coterminal with $A = 142^{\circ}$ .

Studdy Solution

STEP 1

Assumptions1. The given angle is $A =142^{\circ}$ . . We are looking for the least positive angle that is coterminal with $A$ .
3. Two angles are coterminal if they differ by an integer multiple of $360^{\circ}$ .

STEP 2

First, we need to find the least positive angle that is coterminal with $A$ . To do this, we subtract multiples of $360^{\circ}$ from $A$ until we get a positive angle less than $360^{\circ}$ .
$A' = A -360^{\circ} \times n$ where $n$ is an integer and $A'$ is the coterminal angle we are looking for.

STEP 3

Since $A =142^{\circ}$ is already less than $360^{\circ}$ , the least positive angle that is coterminal with $A$ is $A$ itself.
$A' = A =142^{\circ}$ So, the measure of the least positive angle that is coterminal with $A$ is $142^{\circ}$ .

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