Question

In Trig Values of Special angles, how do we know if cos π/4 is $\frac{-\sqrt{2}}{2}$ or $\frac{\sqrt{2}}{2}$ dpending on what quadrant it is?



Pls, explain in detail, I've been trying to understand it for two days :( Thank you.

Answer 1

Ok, so i will try my best to explain.

                              ANSWER

All trigonometric identities namely sin,cos ,tan,sec,cosec , cot are positive in first quadrant.!st quadrant lies between 0 to π/2.

Similarly only sin and cosec are positive in 2nd quadrant.

In 3rd tan and cot are positive

Finally in 4th cos and sec are positive.

The first quadrant basically describes the angle between 0 to π/2.

2nd quadrant from π/2 to π

3rd quadrant from π to 3π/2

4th quadrant from 3π/2 to 2π or can also be written as 3π/2 to 0.

Now, you have asked for cos π/4

As you can see, π/4 lies between 0 to π/2 ie in the first quadrant.

I had said that everything is positive in 1st quadrant ,thus cos π/4 will be positive .So it will be +√2/2 and not -√2/2.

                        Thank you