Question

An acute angle, θ, is in a right triangle such that cos θ = 12/13. What is the Value of csc θ? (100 Points!)

13/12
13/5
5/13
5/12

Answer 1

`\textsf{a)} \quad \text{cosec}\:\theta=(13)/(12)`

Explanation:

Given cosine trigonometric identity:

`\boxed{\cos\theta=(12)/(13)}`

To find the value of cosec θ, use the trigonometric identity:

`\boxed{\text{cosec}\; \theta=(1)/(\cos\theta)}`

Substitute the given value of cos θ into the cosec θ identity:

`\implies \text{cosec}\:\theta=(1)/((12)/(13))`

`\implies \text{cosec}\:\theta=1 / (12)/(13)`

`\implies \text{cosec}\:\theta=1 * (13)/(12)`

`\implies \text{cosec}\:\theta=(13)/(12)`

Therefore, the value of cosec θ is:

`\boxed{\text{cosec}\:\theta=(13)/(12)}`

Answer 2

csc θ = 13/12

Explanation:

cos θ = 12/13

Formula: cos θ = 1/cscθ

Its just the reciprocal.

solve:

1/csc θ = 12/13

csc θ = 13/12