Expert: Sherry Wallin - 11/27/2011

Question
Find all the exact solutions (in radians) for the equation  3tan^2 alpha - 4 = tan alpha.

Answer
Joe~

Substitute tan alpha with x, move everything to the left and get:
3x^2 - x - 4 = 0 now factor the quadratic as (3x - 4)(x + 1)= 0 => 3x - 4 = 0 and x + 1 = 0 =>
x = 4/3, -1 => tan alpha = 4/3, tan alpha = -1 => alpha = tan^-1(4/3), tan^-1(-1)
without a calculator the tangent inverse of -1 should be a no brainer and this occurs at 3pi/4 and at 7pi/4. Now for the tan^-1(4/3) you first note that this will be in QI and QII and using a calculator find that the angle in radians is approximately.295pi and add pi to that getting 1.295pi

Math Prof