How do you find the solution to 2cot^2theta-13cottheta+6=0 if 0<=theta<2pi?

1 Answer
Nghi N
Dec 27, 2016

9^@46, 63^@43, 189^@46, 243^@43

Explanation:

Solve this quadratic equation for cot t
f(t) = 2cot^2 t - 13cot t + 6 = 0
D = d^2 = b^2 - 4ac = 169 - 48 = 121 --> d = +- 11
There are 2 real roots:
cot t = -b/(2a) +- d/(2a) = 13/4 +- 11/4 = (13 +- 11)/4
cot = 24/4 = 6 --> tan t = 1/(cot t) = 1/6
cot t = 2/4 = 1/2 --> tan t = 1/(cot t) = 2
Use calculator and unit circle -->
a. tan t = 1/6 --> t = 9^@46 and t = 180 + 9.46 = 189^@46
b. tan t = 2 --> t = 63^@43 and t = 180 + 63.43 = 243^@43

Answers for (0, 360):
9^@46, 63^@43, 189^@46, 243^@43

Related questions
See all questions in Solving Trigonometric Equations
Impact of this question
2141 views around the world
You can reuse this answer
Creative Commons License