How do you find the solution to tan^2theta-5tantheta+6=0 if 0<=theta<2pi?

1 Answer
Nghi N
Dec 21, 2016

63^@43. 71^@56', 243^@43, 251^@56

Explanation:

Solve this quadratic equation for tan t by the improved quadratic formula (Socratic Search):
tan^2 t - 5tan t + 6 = 0
D = d^2 = b^2 - 4ac = 25 - 24 = 1 --> d = +- 1
There are 2 real roots:
tan t = -b/(2a) +- d/(2a) = 5/2 +- 1/2
tan t = 6/2 = 3 and tan t = 4/2 = 2.
Use calculator and unit circle -->
a. tan t = 3 --> arc t = 71^@56 and arc t = 71.56 + 180 = 251^56
b. tan t = 2 --> arc t = 63^@43, and t = 180 + 63.43 = 243^@43

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