SOLUTION: A is an obtuse angle such that cos(A)=-4/5. Find: 1. Cos(4A). 2. Sin (4A).

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Question 1136950: A is an obtuse angle such that cos(A)=-4/5. Find:
1. Cos(4A).
2. Sin (4A).
Found 2 solutions by Edwin McCravy, Alan3354:
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
A is an obtuse angle such that cos(A)=-4/5. Find:
1. Cos(4A)
A is a QII angle.  We draw a 3-4-5 right triangle in QII.



cos%28A%29=x%2Fr=%28-4%29%2F5=-4%2F5, sin%28A%29=y%2Fr=3%2F5,

cos%282A%29=2cos%5E2%28A%29-1=2%28-4%2F5%29%5E2-1=2%2816%2F25%29-1=32%2F25-25%2F25=7%2F25

2. Sin (4A).
sin%282A%29=2sin%28A%29cos%28A%29=2%283%2F5%29%28-4%2F5%29=-24%2F25

sin%284A%29=2sin%282A%29cos%282A%29=2%28-24%2F25%29%287%2F25%29=-336%2F625

Edwin

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
A is an obtuse angle such that cos(A)=-4/5.
----
The terminal point is in Q2.
======
Find:
1. Cos(4A)
cos(2A) = 2cos^2(A) - 1 = 32/25 - 1 = 7/25
---
cos(4A) = 2*(7/25)^2 - 1 = 98/625 - 1
= -527/625
=====================================
2. Sin (4A)
sin(4A) = sqrt(1 - cos^2(4A))
= sqrt(390625/390625 - 277729/390625)
= sqrt(112896/390625)
= -336/625