Question

HELP WITH THESE QUESTIONS PART 2..

Answer 1

Answer: (a) IV (b) negative (c)
`(\pi)/(3)` (d) A (e)
`-√(3)`

Explanation:

a)
`-(7\pi)/(3)` +
`(6\pi)/(3)` =
`-(\pi)/(3)`

`-(\pi)/(3)` +
`(6\pi)/(3)` =
`(5\pi)/(3)` which is located in Quadrant IV on the Unit Circle

b) tan is
`(sin)/(cos)`. In Quadrant IV, sin is negative and cos is positive so their quotient is negative.

c) the reference angle is the angle from
`(5\pi)/(3)` to 2π which is
`(\pi)/(3)`.

d) Since Quadrant IV is below the x-axis, then another angle would be negative of the reference angle = -tan
`((\pi)/(3))`

e) tan is
`(sin)/(cos)`. tan
`((5\pi)/(3))` =
`-(√(3))/(2)` ÷
`(1)/(2)` =
`-√(3)`

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Answer: C

Explanation:

`(\pi)/(4)` has a reference angle of
`(\pi)/(4)`. All of the angles on the Unit Circle that have a reference angle of
`(\pi)/(4)` are:
`(3\pi)/(4)`,
`(5\pi)/(4)`, and
`(7\pi)/(4)`.

option A is included above. option B reduces to
`(\pi)/(4)`, which is included above. option D reduces to
`(3\pi)/(4)`, which is included above. option C is not included in the family of angles given above.