How do you find the solution to tan^2theta-3tantheta+2=0tan2θ−3tanθ+2=0 if 0<=theta<3600≤θ<360?

1 Answer
Nghi N.
Feb 7, 2017

45^@, 63^@43, 225^@, 243^@4345∘,63∘43,225∘,243∘43

Explanation:

tan^2 t - 3tan t + 2 = 0tan2t−3tant+2=0
Solve this quadratic equation for tan t. Since a + b + c = 0, use shortcut.
tan t = 1 and tan t = c/a = 2tant=ca=2
Use Trig Table, and calculator:
a. Trig Table --> tan t = 1 --> t = 45^@t=45∘
Trig unit circle gives another arc t that has same tan value:
t = 45 + 180 = 225^@t=45+180=225∘
b. Calculator --> tan t = 2 --> t = 63^@43
Unit circle gives another t = 63.43 + 180 = 243^@43t=63.43+180=243∘43
Answers for (0, 360^@)(0,360∘)
45^@, 63^@43, 225^@, 243^@4345∘,63∘43,225∘,243∘43

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