Question

How do you solve `Sinx = 3/4`?

Answer 1

If `sin(x) = 3/4`
`color(white)("XXXXX")`then
`x = arcsin(3/4)`

which can be looked up using a calculator as

`x=0.848 " radians" = 48.59^@`

Answer 2

`sin x = 3/4 = 0.75`

Calculator gives x = 48.59.

The trig unit circle gives another arc x that has the same sin value (0.75):

x = 180 - 48.59 = 131.41 deg

Within the interval (0, 2pi), there are 2 answers: 48.59 and 131.41