Posted by **Bob** on Friday, November 11, 2011 at 11:32am.

If A is between 270degrees and 360degrees, and cos A=12/13, find the exact value of:

sin2a, cos2a, sin1/2a, cos1/2a

- trig/math -
**Steve**, Friday, November 11, 2011 at 12:18pm
since acos(12/13) = .39479, a = 2*pi - .39479 = 5.88839

2a = 11.77678 is in the 4th quadrant, so

sin 2a = 2sin(a)cos(a) = 2(-5/13)(12/13) = -120/169

cos(2a) = cos^2(a) - sin^2(a) = 144/169 - 25/169 = 119/169

a/2 is in the 2nd quadrant

sin(a/2) = √(1/26)

cos(a/2) = -√(25/26)

- trig/math -
**Reiny**, Friday, November 11, 2011 at 12:20pm
if cosA = 12/13 in quadr IV, then

sinA = -5/13

sin 2A = 2sinAcosA = 2(12/13)(-5/13) = -120/169 =

cos 2A = cos^2 A - sin^2 A

= 144/169 - 25/169 = 119/169

we know cos2A = 1 - 2sin^2 A

or

cos A = 1 - 2sin^2 (A/2)

12/13 = 1 - 2sin^2 (A/2)

2sin^2 (A/2) = 1 - 12/13 = 1/13

sin^2 (A/2) = 1/26

sin (A/2) = ±1/√26

but if A is in IV, then A/2 is in II

so sin(A/2) = 1/√26

using

cos A = 2cos^2 (A/2) -1

try the last one.

## Answer This Question

## Related Questions

- trig - Given that cos A = 5/13 and A and B are both acute angles, calculate the ...
- MathS triG - 1 .If tanA=1/3 and tanB=1/7 (both A and B are acute),calculate ...
- maths Pls help trig - 1 .If tanA=1/3 and tanB=1/7 (both A and B are acute),...
- Maths - y = 2[cos1/2(f1 - f2)x][cos1/2(f1 + f2)x] let f1 = 16 let f2 = 12 ...
- Trigonometry - 4. Find the exact value for sin(x+y) if sinx=-4/5 and cos y = 15/...
- Trigonometry - Using exact values, find the value of: a. 12 sin 30 degrees ¨C 6 ...
- trig - Show that 1-cos2A/Cos^2*A = tan^2*A 1-cos2A/Cos^2*A = [Cos^2(A) - Cos(2A...
- trig - CosA x cos2A + ((sin2A)^2)/2cosA
- Math - If sinA=0.5 , what is the value of cos2A and sin2A?
- trig maths - rewrite 7 sin2A – 5 sin A + cos2A = o to solve for A

More Related Questions