QuestionFind 3 angles coterminal with $201^{\circ}$ , 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. . To find coterminal angles, we can add or subtract multiples of $360^{\circ}$ (a complete revolution in degrees) from the given angle.

STEP 2

First, let's find a positive angle that is coterminal with $201^{\circ}$ . We can do this by adding $360^{\circ}$ to $201^{\circ}$ .
$Positive\, Coterminal\, Angle =201^{\circ} +360^{\circ}$

STEP 3

Calculate the positive coterminal angle.
$Positive\, Coterminal\, Angle =201^{\circ} +360^{\circ} =561^{\circ}$

STEP 4

Next, let's find a negative angle that is coterminal with $201^{\circ}$ . We can do this by subtracting $360^{\circ}$ from $201^{\circ}$ .
$Negative\, Coterminal\, Angle =201^{\circ} -360^{\circ}$

STEP 5

Calculate the negative coterminal angle.
$Negative\, Coterminal\, Angle =201^{\circ} -360^{\circ} = -159^{\circ}$

STEP 6

Finally, let's find another positive angle that is coterminal with $201^{\circ}$ . We can do this by adding two multiples of $360^{\circ}$ to $201^{\circ}$ .
$Another\, Positive\, Coterminal\, Angle =201^{\circ} +2 \times360^{\circ}$

STEP 7

Calculate the other positive coterminal angle.
$Another\, Positive\, Coterminal\, Angle =201^{\circ} +2 \times360^{\circ} =921^{\circ}$ So the three different angles that are coterminal with $201^{\circ}$ are $561^{\circ}$ , $-159^{\circ}$ , and $921^{\circ}$ .

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