Question

How do you solve the equation `sintheta=0.91` for `0<theta<2pi`?

Answer 1

`theta ~~ 65.5^@ " and " ~~114.5^@`

Explanation:

Given: `sin theta = 0.91` for `0 < theta < 2pi`

The sine is positive in two quadrants: quadrant 1 & 2

`theta = sin^-1 (0.91) ~~ 65.5^@`

To find `theta` in the 2nd quadrant, subtract this angle from `180^@`:

`theta = 180^@ - 65.5^@ = 114.5^@`

Answer 2

`theta=1.14" or "theta=2`

Explanation:

`"since "sintheta>0" then "theta" is in first or second"`
`"quadrant"`

`theta=sin^-1(0.91)=1.14" radians"larrcolor(red)"first quadrant"`

`"or "theta=(pi-1.14)=2larrcolor(red)"in second quadrant"`

`"solutions are "theta=1.14" or "theta=2to(0,2pi)`