Math  /  Trigonometry

QuestionGiven θ=675, find the following:\text{Given } \theta = -675^\circ, \text{ find the following:} \begin{enumerate} \item[(b)] \text{Find an angle between } 0^\circ \text{ and } 360^\circ \text{ that is coterminal with } \theta. \item[(c)] \text{Find an angle between } -360^\circ \text{ and } 0^\circ \text{ that is coterminal with } \theta. \end{enumerate}

Studdy Solution

STEP 1

1. Coterminal angles differ by full rotations of 360360^\circ.
2. To find a coterminal angle, we can add or subtract 360360^\circ as needed.

STEP 2

1. Find a positive coterminal angle for θ=675\theta = -675^\circ.
2. Find a negative coterminal angle for θ=675\theta = -675^\circ.

STEP 3

To find an angle between 00^\circ and 360360^\circ that is coterminal with 675-675^\circ, we need to add 360360^\circ repeatedly until the angle is within the desired range.

STEP 4

Start by adding 360360^\circ to 675-675^\circ:
675+360=315-675^\circ + 360^\circ = -315^\circ
Since 315-315^\circ is still not within 00^\circ to 360360^\circ, add 360360^\circ again:
315+360=45-315^\circ + 360^\circ = 45^\circ
Now, 4545^\circ is within the range 00^\circ to 360360^\circ.

STEP 5

To find an angle between 360-360^\circ and 00^\circ that is coterminal with 675-675^\circ, we need to subtract 360360^\circ from 675-675^\circ.

STEP 6

Subtract 360360^\circ from 675-675^\circ:
675+360=315-675^\circ + 360^\circ = -315^\circ
Now, 315-315^\circ is within the range 360-360^\circ to 00^\circ.
The angles that are coterminal with θ=675\theta = -675^\circ are: (b) 45\text{(b) } 45^\circ (c) 315\text{(c) } -315^\circ

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