Find the cosine and sine of the angle 135Solutioncosine 135

Find the cosine and sine of the angle = 135°

Solution

cosine 135

It can also be written as cos(90 +45)

cos(A+B)=cos A cosB- sinA sinB

cos(90+45) =cos 90 cos 45 -sin 90sin4 = *(1/sqrt2)- 1*(1/sqrt2) = -1/sqrt2 = -sqrt2/2

cos 135= -sqrt2/2

sin135=sin(90+45)

sin(A+B)=sinAcosB-cosAsinB

sin(90+45)=sin90cos45 +cos90sin45=1(1/sqrt2)+0(1/sqrt2)

                    =1/sqrt2=sqrt2/2

sin 135= sqrt2/2