SOLUTION: I'm kinda stuck on these three identity Questions: Could you explain how to solve these to me. Please and Thankyou.
6. Find the exact value of sin 2 θ given that cos θ
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Question 329512: I'm kinda stuck on these three identity Questions: Could you explain how to solve these to me. Please and Thankyou.
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)
sin(2θ)=?
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?
15. Evaluate sin(π/12)-sin((5π)/12).
*My answer was 1. Am I correct?
Found 2 solutions by Alan3354, nyc_function:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
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)
-------------------------
sin^2 + cos^2 = 1
=
------------------
sin(2t) = 2sin(t)cos(t)
= 2(5/13)*(12/13)
= 120/169
----------
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.
------------------------
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
Answer by nyc_function(2741) (Show Source): You can put this solution on YOUR website!
BIG TIP: Post one question at a time or else no one will reply.
I will do question 6 only.
6. Find the exact value of sin 2 θ given that cos θ = 12/13 and θ is in Quadrant I.
We are in quadrant 1 which means all trig functions are positive. So, there's no need to worry about signs in this case.
Using a right triangle in the first quadrant, we know that cos(theta) = adj/hyp.
Using the Pythagorean Theorem, we also learn that the missing side is 5.
sin(theta) = opp/hyp
sin(theta) = 5/13
cos(theta) = adj/hyp
cos(theta) = 12/13
We now plug it into the formula sin(2θ) = 2sin(θ)cos(θ) and simplify.
sin(2θ) = 2(5/13)(12/13)
sin(2θ) = 2(5/13)(12/13)
sin(2θ) = 120/169
CHOICE B
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