Question

Point P(-2, -7) is on the terminal arm of an angle

0 in standard position. Determine the measure of
0 to the
nearest degree

Answer 1

The measure of angle
`\( \theta \)` to the nearest degree is
`\( \theta \approx 74^\circ \)`.


To determine the measure of angle
`\( \theta \)` to the nearest degree, you can use trigonometric ratios. In standard position, you can calculate the angle using the tangent function:

`\[ \tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}} \]`

For point P(-2, -7), the opposite side is -7, and the adjacent side is -2.

`\[ \tan(\theta) = (-7)/(-2) \]`

Now, find the angle
`\( \theta \)`:

`\[ \theta = \tan^(-1)\left((-7)/(-2)\right) \]`

Using a calculator, you get
`\( \theta \approx 74^\circ \)`.

Therefore, the measure of angle
`\( \theta \)` to the nearest degree is
`\( \theta \approx 74^\circ \)`.