Solve for Theta

Question

tan^4(𝜃) − 34 tan^2(𝜃) + 225 = 0

Answer 1

tan^4(𝜃) − 34 tan^2(𝜃) + 225 = 0

Note that the form of the equation is similar to ax^2 + bx + c = 0

In this case tan^2(𝜃) is our "x." Therefore, we can factor this problem quite easily.

(tan^2(𝜃) - 25)(tan^2(𝜃) - 9) = 0

Both of these factors happen to be difference of squares so we can factor further.

(tan(𝜃) + 5)(tan(𝜃) - 5)(tan(𝜃) + 3)(tan(𝜃) - 3) = 0

Now set each of these factors equal to 0 to get 4 solutions

tan(𝜃) + 5 = 0 tan(𝜃) - 5 = 0 tan(𝜃) + 3 = 0 tan(𝜃) - 3 = 0

tan(𝜃) = -5 tan(𝜃) = 5 tan(𝜃) = -3 tan(𝜃) = 3

𝜃 = arctan(-5) 𝜃 = arctan(5) 𝜃 = arctan(-3) 𝜃 = arctan(3)

You can then evaluate in a calculator based on whether your answer is in degrees or radians