Question

What is the exact value of sin75 degrees

Answer 1

I use my calculator for these kinds of problems, so I can't show any work.

sin75° = 0.965925826...

≈ 0.97

The first answer contains all the digits that fit on my calculator screen and the second answer is rounded to the nearest hundredth (just in case you might want to know).

Hope this helps!

Answer 2

`(√(2)+√(6)  )/(4)`

Explanation:

Using the addition formula for sine

• sin(x + y) = sinxcosy + cosxsiny

sin75° can be expressed as sin(30 + 45)°, thus

sin(30 + 45)°

= sin30°cos45° + cos30°sin45°

= (
`(1)/(2)` ×
`(√(2) )/(2)`) + (
`(√(3) )/(2)` ×
`(√(2) )/(2)`)

=
`(√(2) )/(4)` +
`(√(6) )/(4)`

=
`(√(2)+√(6)  )/(4)`