trigonometric identities

Question

Use trigonometric identities to find the exact value of cos(5π/8).

Answer 1

You first have to notice that 5π/8 is half of 5π/4. If they are asking you to use an identity, it is either a sum, difference double angle or half angle formula.

 

The 1/2 angle formula for cos A/2 = +-sqrt( (1+cos A)/2).

 

So cos 5pi/8 = +-sqrt( (1+cos(5pi/4))/2)

which equals +-sqrt( ( 1- (sqrt2 / 2)) /2)

 

Since 5pi/8 terminates in quadrant 2, the cos (5pi/8) would be the negative answer.

 

This isn't simplified fully, but I'll leave that to you.....if it's necessary at all.

 

Hope this helped.