QuestionFind 3 angles coterminal with $77^{\circ}$ , including at least one negative and one positive angle.

Studdy Solution

STEP 1

Assumptions1. Coterminal angles are angles that share the same terminal side in the standard position (initial side on the positive x-axis). . An angle of $360^{\circ}$ represents a full rotation.
3. We can find coterminal angles by adding or subtracting multiples of $360^{\circ}$ from the given angle.

STEP 2

First, let's find a positive angle that is coterminal with $77^{\circ}$ . We can do this by adding $360^{\circ}$ to $77^{\circ}$ .
$Positive\, Coterminal\, Angle =77^{\circ} +360^{\circ}$

STEP 3

Now, calculate the positive coterminal angle.
$Positive\, Coterminal\, Angle =77^{\circ} +360^{\circ} =437^{\circ}$

STEP 4

Next, let's find a negative angle that is coterminal with $77^{\circ}$ . We can do this by subtracting $360^{\circ}$ from $77^{\circ}$ .
$Negative\, Coterminal\, Angle =77^{\circ} -360^{\circ}$

STEP 5

Now, calculate the negative coterminal angle.
$Negative\, Coterminal\, Angle =77^{\circ} -360^{\circ} = -283^{\circ}$

STEP 6

Finally, let's find another positive angle that is coterminal with $77^{\circ}$ . We can do this by adding two times $360^{\circ}$ to $77^{\circ}$ .
$Another\, Positive\, Coterminal\, Angle =77^{\circ} +2 \times360^{\circ}$

STEP 7

Now, calculate the another positive coterminal angle.
$Another\, Positive\, Coterminal\, Angle =77^{\circ} +2 \times360^{\circ} =797^{\circ}$ So, the three angles that are coterminal with $77^{\circ}$ are $437^{\circ}$ , $-283^{\circ}$ , and $797^{\circ}$ .

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