SOLUTION: I was given the following problem but I am having difficulty with it:
compute the exact values of sin x/2, cos x/2, tan x/2
tan x=3/4, -pi<x<-pi/2
Can you show me the pro
Algebra.Com
Question 818300: I was given the following problem but I am having difficulty with it:
compute the exact values of sin x/2, cos x/2, tan x/2
tan x=3/4, -pi
Can you show me the process of how to solve this?
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
I was given the following problem but I am having difficulty with it:
compute the exact values of sin x/2, cos x/2, tan x/2
tan x=3/4, -pi
***
Identities:
..
Assume reference angle x is quadrant I
You are working with a 3-4-5 right triangle in quadrant I
sin(x)=3/5
cos(x)=4/5
..
=1/√10=√10/10
=√(9/10)=3/√10=3√10/10
..
calculator check:
tan(x)=3/4
x≈36.8698˚
x/2≈18.4349˚
..
sin(x/2)≈sin(18.4349)≈0.3162..
exact value as calculated=√10/10≈0.3162..
..
cos(x/2)≈cos(18.4349)≈0.9486..
exact value as calculated=3√10/10≈0.9486..
..
tan(x/2)=tan(18.4349)≈0.3333..
exact value as calculated=1/3
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