Question

Q 1 PLEASE HELP ME FIGURE THIS OUT 2

Answer 1

Answer:
`(\pi )/(3)`

Explanation:

cot is
`(cos)/(sin)` on the Unit Circle. When is cos =
`(1)/(2)` and sin =
`\frac{√(3)} {2}`? In other words, where is the coordinate
`((1)/(2),\frac{√(3)} {2})` on the Unit Circle?

It occurs at 60° =
`(\pi )/(3)` radians

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Answer: cot θ

Explanation:

sec (90 - θ) * cos θ

=
`(1)/(cos (90 -\theta))` * cos θ

=
`(cos\theta)/(cos(90 - \theta))`

=
`(cos\theta)/(cos90*cos\theta+sin90*sin\theta)`

=
`(cos\theta)/(0*cos\theta+1*sin\theta)`

=
`(cos\theta)/(sin\theta)`

= cot θ

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Answer: BC = √5, AC = 2√5

Explanation:

`\frac{\pi} {3}` = 60°, which means ΔABC is a 30°-60°-90° triangle so we can use the side length formulas: x - x√3 - 2x.

∠C is the 60°. It matches to side AB so: AB = x√3 = √15 ⇒ x = √5

∠A is the 30°. It matches to side BC so: BC = x = √5

∠B is the 90°. It matches to side AC so: AC = 2x = 2(√5) = 2√5

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Answer: k = 4, RS = 12, QS = 28

Explanation:

`(QR)/(MN) = (RS)/(NO)= (QS)/(MO)`

`(24)/(6) = (RS)/(3)= (QS)/(7)`

proportionality constant k can be found with
`(QR)/(MN)` =
`(24)/(6)` = 4

`(QR)/(MN) = (RS)/(NO)`

→ 4 =
`(RS)/(3)`

→ 4(3) = RS

→ 12 = RS

`(QR)/(MN) = (QS)/(MO)`

→ 4 =
`(QS)/(7)`

→ 4(7) = QS

→ 28 = QS