Posted by **Lucy X** on Sunday, December 7, 2008 at 2:34am.

If tan(x)= -(3/4) and x is obtuse, evaluate sin(2x).

How do I get started on this question?

- Math -
**Damon**, Sunday, December 7, 2008 at 5:30am
This angle x is obtuse, between 90 and 180 degrees. Therefore 2x is between 180 and 360.

tan x = -3/4

height = 3

base = 4

hypotenuse = 5 (3,4, 5 right triangle)

so

sin x = 3/5

cos x = -4/5

and we know sin 2x = 2 sin x cos x

so

sin 2x = 2(3/5)(-4/5)

sin 2x = -24/25

- Math -
**drwls**, Sunday, December 7, 2008 at 5:36am
Angles with negative values of the tangent are in the second or fourth quadrant. If it is obtuse (between 90 and 180 degrees), it is in the second quadrant. The supplement of the angle is sin^-1 (3/5)= 36.87 degrees. (Think of a 3,4,5 right reference triangle). The angle x is therefore 143.13 degrees, and its sine is 3/5. Its cosine is -4/5. Use sin 2x = 2 sin x cos x to get the sine of twice the angle.

Sin (2x) = 2(3/5)(-4/5) = -24/25 = -0.96. It is in the fourth quadrant.

## Answer This Question

## Related Questions

- Trig - Given: cos u = 3/5; 0 < u < pi/2 cos v = 5/13; 3pi/2 < v < ...
- precalculus - For each of the following determine whether or not it is an ...
- math - Prove the identity: tan^2O/ 1 + tan^20 = sin^20 I get 1=1, but others ...
- mathematics - evaluate each of the following..sin 130.tan 60/cos 540.tan 230.sin...
- Inverse Functions & Trig. Equations - 7. Evaluate sin[sin^-1(-1/2)]. a. 1/2 b...
- MathsSs triG - Consider sin(x-360)sin(90-x)tan(-x)/cos(90+x) 1.A.SIMPLIFY sin(x-...
- Math - Evaluate *Note - We have to find the exact value of these. That I know to...
- Limit Calculas - Evaluate lim->4 sin(2y)/tan(5y) Here is what I have so far. ...
- calculus - Evaluate lim->4 sin(2y)/tan(5y) Here is what I have so far. I am ...
- Trig Identities - Proving identities: 1) 1+ 1/tan^2x = 1/sin^2x 2) 2sin^2 x-1 = ...

More Related Questions