QuestionFind 3 angles coterminal with $39^{\circ}$ , including at least one negative and one positive angle.

Studdy Solution

STEP 1

Assumptions1. We are looking for angles that are coterminal with $39^{\circ}$ . . Coterminal angles are angles that share the same terminal side in the standard position.
3. We can find coterminal angles by adding or subtracting multiples of $360^{\circ}$ (a complete revolution) to the given angle.

STEP 2

First, let's find a positive angle that is coterminal with $39^{\circ}$ . We can do this by adding $360^{\circ}$ to $39^{\circ}$ .
$Positive\, Coterminal\, Angle =39^{\circ} +360^{\circ}$

STEP 3

Now, calculate the positive coterminal angle.
$Positive\, Coterminal\, Angle =39^{\circ} +360^{\circ} =399^{\circ}$

STEP 4

Next, let's find a negative angle that is coterminal with $39^{\circ}$ . We can do this by subtracting $360^{\circ}$ from $39^{\circ}$ .
$Negative\, Coterminal\, Angle =39^{\circ} -360^{\circ}$

STEP 5

Now, calculate the negative coterminal angle.
$Negative\, Coterminal\, Angle =39^{\circ} -360^{\circ} = -321^{\circ}$

STEP 6

Finally, let's find another positive angle that is coterminal with $39^{\circ}$ . We can do this by adding two multiples of $360^{\circ}$ to $39^{\circ}$ .
$Another\, Positive\, Coterminal\, Angle =39^{\circ} +2 \times360^{\circ}$

STEP 7

Now, calculate the other positive coterminal angle.
$Another\, Positive\, Coterminal\, Angle =39^{\circ} +2 \times360^{\circ} =759^{\circ}$ So, the three angles that are coterminal with $39^{\circ}$ are $399^{\circ}$ , $-321^{\circ}$ , and $759^{\circ}$ .

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