Question

If cos θ = 0.28, find cosec θ - cot θ.

Answer 1

Given:

cos θ = 0.28

Step 1: Find sin⁡ θ

sin θ = `sqrt(1 − cos^2 θ)​`

sin θ = `sqrt(1 − (0.28)^2)​ = sqrt(1 − 0.0784) = sqrt0.9216 = 0.96`

Step 2: Find csc⁡ θ and cot θ

csc θ = `1/sin θ = 1/0.96 = 1.0417`

tan θ = `sin θ /cos θ = 0.96/0.28 ≈ 3.4286`

cot θ = `1/tan θ ≈ 0.2917`

Step 3: Calculate csc⁡ θ − cot⁡ θ

csc θ − cot θ ≈ 1.0417 − 0.2917 = 0.75

csc θ − cot θ = `3/4`