Can you explain why this is the answer

Ok, I know that if I am asked to solve: tan(x)+1=0 I am supposed to write it as tan(x)=-1 and that the answer is 3pi/4 or 7pi/4. I just do not understand how to get the answer! Does it have to do something with the unit circle? If so, how do I get it?!

If I have tan²3x= 3 how would I solve this?

THANKS :)

Once you have re-arranged it to tan(x) = -1 you then have to use the inverse tan function (on a calculator) to find x:

This should be on all scientific/graphic calculators and looks like this:

tan^-1

So to find x you do: tan^-1(-1) = -pi/4
To make this positive you add pi (explained by trigonometrical graphs) and you will get: 3pi/4
To get the 'or 79i/4' you have to add another pi - this works because tan graph repeats itself every pi radians.

Therefore the answers are: 3pi/4 or 7pi/4

(NOTE - as your answer is in radians - due to the pi signs, you must make sure your calculator is set up in RAD mode before you start doing the calculations)

Hope that helps!

Remember CAST There are four quadrants in the unit circle

CAST will show you which trig functions are positive.

Starting in the fourth quadrant the Cosine is positive
go anticlockwise to the first quadrant where ALL are postive
move the the Second quadrant where the Sine is positive
move to the Third quadrant where the Tangent is positive

In your problem you know that tan x = -1
CAST tells you that the tangent is positive in the |First and third quadrants so your tanx's must be in the second and fourth quadrants i.e. between pi/2 and pi and 3pi/2 and 2pi

Tan^2(3x) = 3
Tan(3x) = root(3) = 1.732 = 60 degrees so x = 20 degrees or pi/3

yes, tan x + 1 = 0 ==> tan x = -1 ==> 3pi/4 or 7pi/4 from the unit circle
(these are the angles where y = -x

you MUST know the special angles on the unit circle for exact values: