Question

Trigonometry, please provide a simple explanation

Answer 1

C

Explanation:

cosecΘ =
`(1)/(sin0)` =
`(2)/(√(3) )` ( cross- multiply )

2sinΘ =
`√(3)` ( divide both sides by 2 )

sinΘ =
`(√(3) )/(2)` , then

Θ =
`sin^(-1)` (
`(√(3) )/(2)` ) = 60°

Answer 2

C. 60°

Explanation:

by definition, cosec(θ) is the reciprocal of sin(θ)

In other words ,

`\text{cosec} \left( \theta \right) =(1)/(\sin \theta )`

Then

`\text{cosec} \left( \theta \right) =(2)/(√(3) )`

`\Longleftrightarrow (1)/(sin \left( \theta \right) ) =(2)/(√(3) )`

`\Longleftrightarrow sin \left( \theta \right) =\frac{√(3) } {2}`

Then

θ = 60°