Question

Q 2 PLEASE HELP ME FIGURE THIS OUT 2.0

Answer 1

Answer: II, positive,
`(\pi)/(3)`, C,
`(√(3))/(2)`

Explanation:

a)
`(2\pi)/(3)` = 120° which is located in Quadrant II

b) In Quadrant II, cos is negative and sin is positive

c) In order to reach the x-axis, it would need to go to 180°. 180 - 120 = 60° ... or ... it would need to go to π. π -
`(2\pi)/(3)` =
`(\pi)/(3)`

d) sin
`(2\pi)/(3)` =
`(√(3))/(2)`. What other angle on the Unit Circle has that value for sin?
`(\pi)/(6)`

e) sin
`(2\pi)/(3)` =
`(√(3))/(2)`

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Explanation:

(16, -18) are the legs of the triangle. Use Pythagorean Theorem to find the hypotenuse. 16² + (-18)² = c² ⇒ 580 = c² ⇒
`2√(145)` = c

adjacent = 16, opposite = -18, hypotenuse =
`2√(145)`

Answers:

sin =
`(opposite)/(hypotenuse)` =
`(-18)/(2√(145))` =
`(-9)/(√(145)) * (√(145))/(√(145))` =
`\frac{-9√(145)} {145}`

cos =
`(adjacent)/(hypotenuse)` =
`(16)/(2√(145))` =
`(8)/(√(145)) * (√(145))/(√(145))` =
`\frac{8√(145)} {145}`

tan =
`(opposite)/(adjacent)` =
`(-18)/(16)` =
`-(9)/(8)`

csc =
`(hypotenuse)/(opposite)` =
`(2√(145))/(-18)` =
`(√(145))/(-9)` =
`-\frac{√(145)} {9}`

cos =
`(hypotenuse)/(adjacent)` =
`(2√(145))/(16)` =
`(√(145))/(8)`

cot =
`(adjacent)/(opposite)` =
`(16)/(-18)` =
`-(8)/(9)`