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

Answer:

$\theta = 14.1\ degrees$

$846\ minutes$

Step-by-step explanation:

Given

$csc(\theta) = 4.1191$

Required

Solve for $\theta$

$csc(\theta) = 4.1191$

$csc(\theta) = \frac{1}{sin(\theta)}$

So, we have:

$\frac{1}{sin(\theta)} = 4.1191$

Invert both sides

$sin(\theta) = \frac{1}{4.1191}$

$sin(\theta) = 0.2428$

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:

$14.1\ degrees = 14.1 * 60\ minutes$

$14.1\ degrees = 846\ minutes$