Answer: ![\frac{\pi }{3}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cpi%20%7D%7B3%7D)
<u>Step-by-step explanation:</u>
cot is
on the Unit Circle. When is cos =
and sin =
? In other words, where is the coordinate
on the Unit Circle?
It occurs at 60° =
radians
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Answer: cot θ
<u>Step-by-step explanation:</u>
sec (90 - θ) * cos θ
=
* cos θ
= ![\frac{cos\theta}{cos(90 - \theta)}](https://tex.z-dn.net/?f=%5Cfrac%7Bcos%5Ctheta%7D%7Bcos%2890%20-%20%5Ctheta%29%7D)
= ![\frac{cos\theta}{cos90*cos\theta+sin90*sin\theta}](https://tex.z-dn.net/?f=%5Cfrac%7Bcos%5Ctheta%7D%7Bcos90%2Acos%5Ctheta%2Bsin90%2Asin%5Ctheta%7D)
= ![\frac{cos\theta}{0*cos\theta+1*sin\theta}](https://tex.z-dn.net/?f=%5Cfrac%7Bcos%5Ctheta%7D%7B0%2Acos%5Ctheta%2B1%2Asin%5Ctheta%7D)
= ![\frac{cos\theta}{sin\theta}](https://tex.z-dn.net/?f=%5Cfrac%7Bcos%5Ctheta%7D%7Bsin%5Ctheta%7D)
= cot θ
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Answer: BC = √5, AC = 2√5
<u>Step-by-step explanation:</u>
= 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
<u>Step-by-step explanation:</u>
![\frac{QR}{MN} = \frac{RS}{NO}= \frac{QS}{MO}](https://tex.z-dn.net/?f=%5Cfrac%7BQR%7D%7BMN%7D%20%3D%20%5Cfrac%7BRS%7D%7BNO%7D%3D%20%5Cfrac%7BQS%7D%7BMO%7D)
![\frac{24}{6} = \frac{RS}{3}= \frac{QS}{7}](https://tex.z-dn.net/?f=%5Cfrac%7B24%7D%7B6%7D%20%3D%20%5Cfrac%7BRS%7D%7B3%7D%3D%20%5Cfrac%7BQS%7D%7B7%7D)
proportionality constant k can be found with
=
= 4
![\frac{QR}{MN} = \frac{RS}{NO}](https://tex.z-dn.net/?f=%5Cfrac%7BQR%7D%7BMN%7D%20%3D%20%5Cfrac%7BRS%7D%7BNO%7D)
→ 4 = ![\frac{RS}{3}](https://tex.z-dn.net/?f=%5Cfrac%7BRS%7D%7B3%7D)
→ 4(3) = RS
→ 12 = RS
![\frac{QR}{MN} = \frac{QS}{MO}](https://tex.z-dn.net/?f=%5Cfrac%7BQR%7D%7BMN%7D%20%3D%20%5Cfrac%7BQS%7D%7BMO%7D)
→ 4 = ![\frac{QS}{7}](https://tex.z-dn.net/?f=%5Cfrac%7BQS%7D%7B7%7D)
→ 4(7) = QS
→ 28 = QS