Question 329512
6. Find the exact value of sin 2 θ given that cos θ = 12/13 and θ is in Quadrant I.
a. -120/169 
b. 120/169 
c. 60/169 
d. -60/169 
*sin(2θ)=2sin(θ)cos(θ)
sin(2θ)=2sin(θ)cos(12/13)
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sin^2 + cos^2 = 1
{{{sin(t) = sqrt(1 - cos^2(t))}}}
= {{{sqrt(1 - (144/169)) = sqrt(25/169) = 5/13}}}
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sin(2t) = 2sin(t)cos(t)
= 2(5/13)*(12/13)
= 120/169
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8. Find the value of the tan of a/2 given that cos a = -4/5 and a is in Quadrant II. 
a. 3
b. 1/2 
c. -2 
d. -1/2 
*tan(a/2)=1-cos(a)/sin(a)
tan(a/2)=1-cos(-4/5)/sin(1/5)
tan(a/2)=? 
14. Evaluate sin 165° + sin 105°
*My answer was -√(2)/2. Am I correct?
You can use a calculator to see that's not correct.
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15. Evaluate sin(π/12)-sin((5π)/12).
*My answer was 1. Am I correct?
No.  Use a calculator to see that it's -sqrt(2)/2