Question

if cos theta is equals to minus 3 upon 5 and theta lies between 180 to 270 the values of other five trigonometric functions and hence evaluate cosec theta + cot theta upon sec theta minus 10 theta​

Answer 1

Answer:

Step-by-step explanation:

if cos theta is equals to minus 3 upon 5 and theta lies between 180 to 270 the values of other five trigonometric functions and hence evaluate cosec theta + cot theta upon sec theta minus 10 theta​

Cosθ  = -3/5    = -0.6

θ lies between 180° to 270° => 3rd Quadrant

Sinθ = √1 - Cos²θ  = √( 1 - (3/5)²  =  √16/25 =  - 4/5 = -0.8

as Sinθ is -ve in 3rd Quadrant

Tanθ  = Sinθ/Cosθ  = (-4/5)/(-3/5) = 4/3 = 1.333

Cosecθ  = 1/Sinθ  = 1/(-4/5) = -5/4 = -1.25

Secθ  = 1/Cosθ  = 1/(-3/5) = -5/3 = -1.667

Cotθ  =  Cosθ/ Sinθ = (-3/5)/(-4/5) = 3/4 = 0.75

Cosecθ + Cotθ = -1.25 + 0.75 = -0.5

Secθ - Tanθ = -5/3 - 4/3  = -9/3 = 3

(Cosecθ + Cotθ)/(Secθ - Tanθ) = 0.5/3 = 1/6

Answer 2

Step-by-step explanation:

180degree<theta<270degree,

It means 4th Quadrant.

In 4th Quadrant tan and cot only positive and others are negative..

Hope this answer will help you..