HOMEWORK

In quadrant III    sin and cos are BOTH negative

sin^2 + cos^2 = 1

sin^2 = 1- c0s^2 = 1- 9/16= 7/16

sin =- sqrt 7  /4

csc = 1/sin = -  4 / sqrt 7     tan = sin / cos  = - sqrt7/4 / -3/4 = 4 sqrt 7  /12 = sqrt7/3

Sorry....you wanted cot    = 1/tan = 3/sqrt7

Let θ be an angle in quadrant III such that cosθ=(−3/4). Find the exact values of cscθ and cotθ.

cscθ =  - 4 /√[ 4^2 - 3^2]    = - 4 /√ [ 7]    =   - [ 4√ ( 7)  / 7 ]  =  -(4/7) √ [ 7]

cotθ  =   3 / √ [ 7]  =  (3/7) √ [ 7 ]