SOLUTION: If sinA= -3/5 with A in quadrant 3, find the following: A.)cos A/2 B.)sin A/2 c.)sec A/2 d.)csc A/2

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Question 1074376: If sinA= -3/5 with A in quadrant 3, find the following:
A.)cos A/2
B.)sin A/2
c.)sec A/2
d.)csc A/2
Answer by sachi(548) About Me  (Show Source):
You can put this solution on YOUR website!
If sinA= -3/5 with A in quadrant 3, find the following:
A.)cos A/2
B.)sin A/2
c.)sec A/2
d.)csc A/2
we know cosA=sqrt(1-sin^2A)=sqrt(1-9/25)=-4/5 (3 quadrant)
we also know that cosA= 2cos^2A/2-1=1-2sin^2A/2
so 2cos^2A/2-1=-4/5
or 2cos^2A/2=1-4/5=1/5
or cos^2A/2=1/10
or cosA/2=-sqrt(1/10)..A
& secA/2=-sqrt10 .......C
now
1-2sin^2A/2=-4/5
2sin^2A/2=1+4/5=9/5
sin^2A/2=9/10
sinA/2=-sqrt(9/10)=-3/sqrt10..B
& cscA/2=-sqrt10/3 .......D
ok