So, anyone good with trig functions and the quadrants? For ex; .

Hi Chirs, I am just wondering why you blanked this one?

Has it been asked somewhere else?

OOPS...sorry.....!!!!!

I didn't look at it .....I thought it was the same question I had answered elsewhere....

My bad !!!!

So, anyone good with trig functions and the quadrants? For ex; .

\(tan​\theta= -1, sin\theta<0\)

What is sine and cosine ratios?

Well, tan is negative in the second and forth quadrants   

 (I remember this with  All Stations To Central)

Sin is negative in the third and forth quadrant.

So tan and sin are both negative only in the 4th quadrant. So that is where the answer has to lie.

Now tan(theta)=+1 when theta = 45 degrees.

So what is the 4th quadrant equivalent?

360-45 = 315 degrees.

So then answer is 

\(\theta=315^\circ+360n\qquad n \in Z\qquad (n\; is \;an\; integer)\)

As Melody has said, "theta"  is a 4th quadrant angle

tangent  = y / x  =    -1    .... so......x = 1     and   y  =  - 1

And  r =   sqrt (x^2 + y^2)  =  sqrt [ 1^2 + (-1)^2 ]  = sqrt (2)

Sine  =  y / r  =  -1 / sqrt (2)

Cosine  =  x / r  =   1 /  sqrt(2)