Harder trig equations

Tan kx = -1/ root 3, where k is constant and k > 0, has a solution at x=60

1) find a possible value of k
2) state whether this is the only possible value of k

Reply 1

Nitrotoluene

Original post

by Toomanyenny

Tan kx = -1/ root 3, where k is constant and k > 0, has a solution at x=60
1) find a possible value of k
2) state whether this is the only possible value of k

To solve tan(kx) = -1/√3 where x = 60, we start with tan(60k) = -1/√3. Because tan(30°) = 1/√3, we search for angles in the second and fourth quarters where the tangent has the value -1/√3. After we locate these angles, we set 60k equal to each angle and solve for k, keeping only the positive values. Because the tangent function repeats every 180°, there are infinite possible answers, so we find infinite positive k values that work.

Ciao,
Sandro

(edited 1 month ago)