How do you express cos( (3 pi)/ 2 ) * cos (( 5 pi) /4 ) without using products of trigonometric functions?

2 Answers
Feb 26, 2016

0

Explanation:

From knowledge of the graph of cosx , we know that

cos((3pi)/2) = 0

and cos((5pi)/4) = -cos(pi/4) = -1/sqrt2

rArr cos((3pi)/2) . cos((5pi)/4) = 0.(-1/sqrt2) = 0

Feb 26, 2016

It is equivalent to 0.

Explanation:

To express cos(3pi/2)*cos(5pi/4), without using trigonometric functions, we should first find value of cos(3pi/2) and cos(5pi/4) separately.

cos(3pi/2) is equal cos((3pi)/2-2pi) or cos(-pi/2), which is equal to cos(pi/2). But as latter is equal to zero,

cos((3pi)/2)=0

Although, cos((5pi)/4)=cos(2pi-(5pi)/4)=cos((3pi)/4)=-cos(pi/4)=(-1/sqrt2)

cos(3pi/2)*cos(5pi/4) will still be 0, as cos((3pi)/2)=0