Question

Please help IM OFFERING ALOT OF POINTS !!!!

Answer 1

Answer:

cos 2Ф = - 161/289 , tan 2Ф = - 240/161

Step-by-step explanation:

* Lets explain how to solve the problem

∵ cos Ф = - 8/17

∵ Ф lies in the 3rd quadrant

- In the 3rd quadrant sin and cos are negative values, but tan is

 a positive value

∵ sin²Ф + cos²Ф = 1

∴ sin²Ф + (-8/17)² = 1

∴ sin²Ф + 64/289 = 1

- Subtract 64/289 from both sides

∴ sin²Ф = 225/289 ⇒ take √ for both sides

∴ sin Ф = ± 15/17

∵ Ф lies in the 3rd quadrant

∴ sin Ф = -15/17

∵ cos 2Ф = 2cos²Ф - 1 ⇒ the rule of the double angle

∵ cos Ф = - 8/17

∴ cos 2Ф = 2(-8/17)² - 1 = (128/289) - 1 = - 161/289

* cos 2Ф = - 161/289

∵ tan 2Ф = sin 2Ф/cos 2Ф

∵ sin 2Ф = 2 sin Ф × cos Ф

∵ sin Ф = - 15/17 and cos Ф = - 8/17

∴ sin 2Ф = 2 × (-15/17) × (-8/17) = 240/289

∵ cos 2Ф = - 161/289

∴ tan 2Ф = (240/289)/(-161/289) = - 240/161

* tan 2Ф = - 240/161