The exact values of csc(θ) and cot(θ) are -5/4 and 3/4 respectively.
" A trigonometric function that for an acute angle is the ratio between the hypotenuse of a right triangle of which the angle is considered part and the leg opposite the angle is called csc and The length of the adjacent side divided by the length of the side opposite the angle in a right-angled triangle is called cot"
Given,
theta lies in the 3rd quadrant.
In 3rd quadrant, cos theta is negative.
cosec theta is negative.
cot theta is positive.
[tex]\cos \theta = -3/5\\ \sin^2\theta + cos^2\theta = 1\\ \sin^2\theta = 1-9/25 = 16/25\\sin\((\theta)= -4/5[/tex]
So, cosecθ = -5/4
Similarly,
[tex]cosec^2\theta - cot^2\theta = 1\\ cot^2\theta = 25/16-1 = 3/4[/tex]
Hence, of csc(θ) and cot(θ) are -5/4 and 3/4 respectively.
To know more about csc and cot here
https://brainly.in/question/19354858
#SPJ2
