Question

How do you find the solution to `tan^2theta-3tantheta+2=0` if `0<=theta<360`?

Answer 1

`45^@, 63^@43, 225^@, 243^@43`

Explanation:

`tan^2 t - 3tan t + 2 = 0`
Solve this quadratic equation for tan t. Since a + b + c = 0, use shortcut.
tan t = 1 and `tan t = c/a = 2`
Use Trig Table, and calculator:
a. Trig Table --> tan t = 1 --> `t = 45^@`
Trig unit circle gives another arc t that has same tan value:
`t = 45 + 180 = 225^@`
b. Calculator --> tan t = 2 --> t = 63^@43
Unit circle gives another `t = 63.43 + 180 = 243^@43`
Answers for `(0, 360^@)`
`45^@, 63^@43, 225^@, 243^@43`