Question

Q 2 PLEASE HELP ME FIGURE THIS OUT 2

Answer 1

Answer: IV, positive, - sec
`(\pi)/(4)`,
`√(2)`

Explanation:

a) Convert radians into degrees to see which quadrant it is in.

[text]\frac{\pi} {180}[\text]=[text]\frac{15\pi}{4x}[\text]

π(4x) = 180(15π)

x =
`\frac{180(15\pi)} {4\pi}`

x = 675°

675° - 360° = 315°, which is located in Quadrant IV.

b) The coordinate (cos θ, sin θ) for 315° is:
`(\frac{√(2)} {2},-\frac{√(2)} {2})`

sec =
`(1)/(cos)` =
`(2)/(√(2))` which is positive

c) Since the given angle is in Quadrant IV, which is closest to the x-axis at 360° = 2π, the reference angle can be found by subtracting the least nonegative angle
`\frac{7\pi} {4}` from 2π:
`\frac{8\pi} {4}` -
`\frac{7\pi} {4}` =
`\frac{\pi} {4}`

d) the reference angle is below the x-axis so the given angle is equal to the negative of the reference angle: - sec
`\frac{\pi} {4}`.

e) sec
`\frac{7\pi} {4}` =
`(2)/(√(2))` =
`(2)/(√(2))*(√(2))/(√(2))`=
`(2√(2))/(2)` =
`√(2)`