Find cot θ if csc θ = sqrt 5/2 and tan θ > 0

Solution:

Given, cosec θ = sqrt(5/2) , we have cot θ = sqrt(cosec² θ - 1)

= sqrt{(5/2)² - 1) = sqrt( 21/4)

Now cot θ = sqrt(21/4)

Example: Find sin θ and cos θ if tan θ = 3/4

Given that, tan θ = 3/4, we have sec θ = sqrt(1 +tan²θ)

⇒ sec θ = sqrt{1 + (3/4)²} = sqrt(25/16) = 5/4

∴ cos θ = 1 / sec θ = 1/ (5/4) = 4/5

sin θ = sqrt ( 1 - cos² θ) = sqrt{ 1 - (4/5)²} = sqrt(9/25) = 3/ 5

Find cot θ if csc θ = sqrt 5/2 and tan θ > 0

Summary:

The value of cot θ if csc θ = sqrt 5/2 and tan θ > 0 is sqrt(21/4)