Posted by **Mandy** on Tuesday, February 7, 2012 at 8:55pm.

Help please! Thank you!

If csc(theta)= -2 and theta lies in Quadrant III, find tan(theta).

- Trig -
**Reiny**, Tuesday, February 7, 2012 at 11:06pm
cscØ = -2

sinØ = -1/2, Ø in III

Ø = 210°

then tan 210° = 1/√3

(I sketched the right-angled triangle in quad III with sides

1 - √3 - 2, for which you should know the ratios.

from the CAST rule I knew that the tangent in III is +

- Trig -
**Bosnian**, Wednesday, February 8, 2012 at 12:41am
In Quadrant III

sin ( theta ) , cos ( theta ) , sec ( theta ) and csc( theta ) are negative.

tan ( theta ) = sin ( theta ) / cos ( theta )

are positive.

tan ( theta ) = + OR -1 / sqrt [ csc ( theta ) ^ 2 - 1 ]

tan ( theta ) = + OR -1 / sqrt [ ( -2 ) ^ 2 - 1 ]

tan ( theta ) = + OR -1 / sqrt ( 4 - 1 )

tan ( theta ) = + OR -1 / sqrt ( 3 )

In Quadrant III

tan ( theta ) are positive so:

tan ( theta ) = 1 / sqrt ( 3 )

## Answer This Question

## Related Questions

- trig - If sin theta is equal to 5/13 and theta is an angle in quadrant II find ...
- trig - If theta is the measure of an angle in standard position with the given ...
- Math - 1. Let (-7, 4) be a point on the terminal side of (theta). Find the exact...
- Trigonometric Functions - Determine the Value of all six trigonometric functions...
- Trig - If tan theta = a/b, where a and b are positive, and if theta lies in ...
- trig - Let (theta) be an angle in quadrant II such that csc(theta)=8/5 Find the ...
- trig - Let (theta) be an angle in quadrant II such that csc(theta)=8/5 Find the ...
- math - if csc theta= -5/3 and theta has its terminal side in quadrant III, find ...
- Precalculus(NEED HELP ASAP PLEASE!!) - cot(theta)= 3 pi < theta < 3pi/2 ...
- trig - Find csc(theta), tan (theta), and cos (theta), where theta is the angle ...

More Related Questions