Question

Use a calculator to find a value of θ between 0° and 90° that satisfies the statement. Write your answer in degrees and minutes rounded to the nearest minute.

csc(theta)= 4.1191

Answer 1

`\theta = 14.1\ degrees`

`846\ minutes`

Explanation:

Given

`csc(\theta) = 4.1191`

Required

Solve for
`\theta`

`csc(\theta) = 4.1191`

`csc(\theta) = (1)/(sin(\theta))`

So, we have:

`(1)/(sin(\theta)) = 4.1191`

Invert both sides

`sin(\theta) = (1)/(4.1191)`

`sin(\theta) = 0.2428`

Take
`sin^(-1)` of both sides

`sin^(-1) sin(\theta) = sin^(-1)0.2428`

`\theta = sin^(-1)0.2428`

`\theta = 14.0518577574`

`\theta = 14.1\ degrees` --- approximated

Convert to minutes:

`1\ degree = 60\ minutes`

So:

`14.1\ degrees = 14.1 * 60\ minutes`

`14.1\ degrees = 846\ minutes`