Question

Use identities to find the value of each expression.

5) Find cot 0 and tan 0
to find the value of each expression.
if sec 0 = 2 and sin 0 > 0.

Answer 1

cot 0 = √3/3 and tan 0 = √3

Explanation:

We can use the following trigonometric identities:

cot θ = 1/tan θ

sec^2 θ = 1 + tan^2 θ

Given sec θ = 2 and sin θ > 0, we can use the identity sec^2 θ = 1 + tan^2 θ to find tan θ:

sec^2 θ = 1 + tan^2 θ

2^2 = 1 + tan^2 θ

tan^2 θ = 3

tan θ = √3

Now that we know tan θ, we can use the identity cot θ = 1/tan θ to find cot θ:

cot θ = 1/tan θ

cot θ = 1/√3

cot θ = √3/3

Therefore, cot 0 = √3/3 and tan 0 = √3.