Question

Use a calculator to find a decimal approximation for the following trigonometric function.

sin 43°24' ≈

​(Simplify your answer. Type an integer or a decimal. Round to eight decimal places as​ needed.)

SHOW YOUR WORK.

Answer 1

converting
43°24' intodegrees, we get

43°24' = 43° + 24'/60 = 43.4°

putting sin(43.4)into calculator to 8 decimal places

sin(43°24') = sin(43.4) = 0.68708751

Answer 2

`\text{sin}(43.4^(\circ))\approx 0.68708751`

Explanation:

We are asked to evaluate the given trigonometric expression
`\text{sin}(43^(\circ)24')`.

We can see that our given angle is in degrees and minutes, so we will convert measure of minutes into degrees by dividing 24 by 60 as:

`(24)/(60)=0.4^(\circ)`

Now, we will find the value of our given expression.

`\text{sin}(43.4^(\circ))=0.687087510804`

Round to eight decimal places:

`\text{sin}(43.4^(\circ))\approx 0.68708751`

Therefore, the value of the given expression would be
`0.68708751`.