Question

Using the identity sin? 0 + cos²0 1, find the value of sin 0, to the nearesthundredth, if cos 0 = 0.52 and 3

Answer 1

we have that

sin^2(x)+cos^2(x)=1

we have

cos(x)=0.52

the angle lie in the IV quadrant

substitute

sin^2(x)+0.52^2=1

sin^2(x)=0.7296

sin(x)=(+/-)0.85

but

the angle lie in IV quadrant

so

is negative

sin(x)=-0.85

Part 2

cos(x)=-0.54

III quadrant

the sine is negative too

substitute

sin^2(x)+(-0.54)^2=1

sin^2(x)=0.7084

sin(x)=-0.84