Question

Given cos (pi/5)=0.809
What is cos(4pi/5)?
[I got 0.809 by picturing it on the unit circle, but the answer says it is -0.809] Where did I go wrong?

Answer 1

Cos(4*pi/5)=cos((5*pi-pi)/5)
Right?

Answer 2

=cos(5*pi/5-pi/5)=cos(pi-pi/5)=-cos(pi/5)
Right?

Answer 3

It is in second quadrant?
Right?

Answer 4

In second quadrant cos in negative

Answer 5

Given cos (pi/5)=0.809
What is cos(4pi/5)?

It might help you visualize this problem more clearly were you to sketch this situation. Angle pi/5 is in Quadrant I, whereas angle 4pi/5 is in Quadrant II.

How are angles pi/5 and 4pi/5 related to one another?

Please share your sketch.

Answer 6

I m frm an android phone

Answer 7

Not possible to draw

Answer 8

@chau88: Again, I suggest the following:

Given cos (pi/5)=0.809
What is cos(4pi/5)?

It might help you visualize this problem more clearly were you to sketch this situation. Angle pi/5 is in Quadrant I, whereas angle 4pi/5 is in Quadrant II.

How are angles pi/5 and 4pi/5 related to one another?

A graph might tell you almost instantly what the answer to this question is.

Given that cos pi/5 = 0.809, we can deduce immediately that the triangle formed by the angle pi/5, radius / hypotenuse of 1, has "adjacent side" equal to 0.809. Draw this triangle as accurately as you can. Next, flip this triangle around the vertical axis to form a new triangle that also has a radius / hypotenuse of 1. What is the length of the "adjacent side" of this new triangle? Is the adjacent side positive or negative? Why?

Answer 9

@Mathmale, thank you very much. I think I got it now. I just misread the graph I drew. Because on the unit circle, I know that cos x is represented by the horizontal distance from the vertical axis, and I misread it.