A-Level Maths Trig Addition Formula

tan((pi/2)-x)=-4
Help?
I have no idea how you get 2.90 and 6.04
tan pi/2 is undefined so how is there still solutions, I know it's moved up 4 (as i've seen on a graph) but how do you work this out?

Reply 1

ran-dumb

This isn’t actually trig addition, and has nothing to do with moving up 4. Think of the pi/2-x as one thing. Thinking of the REGULAR tan graph, what radian values of this give you a final answer of -4? Set pi/2-x equal to that and solve

Reply 2

davros

Original post by Meggggggggggg

tan((pi/2)-x)=-4
Help?
I have no idea how you get 2.90 and 6.04
tan pi/2 is undefined so how is there still solutions, I know it's moved up 4 (as i've seen on a graph) but how do you work this out?

I think you're getting yourself confused here - this isn't really about graph transformations, and you shouldn't need to worry about tan(pi/2) in isolation.

If you think about a right-angled triangle in which one of the unknown angles is 'x', then the remaining angle is just (pi/2) - x. So you can see that if your triangle isn't degenerate (x = 0 or x = pi/2), then whenever tan x is defined, so is tan((pi/2) - x).

In fact, if you label your triangle so that tan x = opposite / adjacent (where 'opposite' = side opposite x) then you can see that:

tan((pi/2) - x) = adjacent / opposite = cot x = 1 / tan x

so that your problem is equivalent to solving cot x = -4 or tan x = -1/4.