Posted by **Yulieth** on Sunday, November 20, 2011 at 8:24pm.

given sinθ=-5/13 and π<θ<3π/2 find

sin2θ

cos( θ-4π/3)

sin(θ/2)

can some1 explain to me how to do these?

- math -
**Henry**, Tuesday, November 22, 2011 at 8:11pm
sinA = -5/13 = Y/r,

X^2 + Y^2 = r^2,

X^2 + (-5)^2 = (13)^2,

X^2 + 25 = 169,

X^2 = 169 - 25 = 144,

X = +- 12.

X = -12 Because it places our resultant

vector in the required quadrant(Q3).

(X,Y) = (-12,-5).

tanA = Y/X = --5/-12 = 0.416666,

A = 22.62 Deg. ,

A = 22.62 + 180 = 202.62(Q3).

180 < 202.62 < 270. Q3.

sin(2A) = sin(405.24) = 0.710.

cos(A-4pi/3) = cos(202.62-240) = 0.7946

sin(A/2) = +- sqrt((1-cosA)/2) =

sqrt((1-cos202.62)/2) = 0.9806

- math -
**Henry**, Wednesday, November 23, 2011 at 3:25pm
Correction:

sinA = -5/13 = Y/r,

A = 157.38 Deg.

sin(2A) = sin(314.76) = -0.710.

cos(A-4pi/3)=cos(157.38-240)=0.1284

sin(A/2) = +- sqrt((1-cosA)/2) =

sqrt((1-cos157.38)/2 = 0.9806.

## Answer this Question

## Related Questions

- trigonometry - given tanθ= -2√10/3 and π/2<θ< π ...
- mathematics - given sinθ=-5/13 and π<θ<3π/2 find sin2...
- Precalc/Trig - Sorry there are quite a few problems, but I just need to know if ...
- trig - cosθ =5/13 with -π/2 < θ <0 find each of the ...
- math - if cosθ=2/3 and tanθ<0 find the exact value sin(θ-5&#...
- Math - Calculus - The identity below is significant because it relates 3 ...
- trigonometry - if cosθ=2/3 and tanθ<0 find the exact value sin(&#...
- trigonometry - tanθ= -2sqrt10/3 and π/2<θ< π find a. ...
- TRIGONOMETRY - Can you check my work, please? This is for a trig study guide for...
- mathematics - given tanθ= -2√10/3 and π/2<θ< π ...

More Related Questions