if sin 20=0.2, what is cos 70?
2 Answers
sciencesolve | Teacher | (Level 3) Educator Emeritus
Notice that `70^o` and `20^o` are complementary angles since the sum measures `90^o` : `20^o+70^o = 90^o.`
You may write `20^o = 90^o - 70^o` , hence `sin 20^o = sin (90^o - 70^o).` You should use the following formula to expand `sin(90^o - 70^o) ` such that:
`sin(alpha - beta) = sinalpha*cos beta - sin beta*cos alpha`
`sin (90^o - 70^o) = sin 90^o*cos 70^o - sin 70^o * cos 90^o`
Since `sin 90^o = 1` and `cos 90^o = 0` then `sin (90^o - 70^o) =cos 70^o.`
Since `sin 20^o = sin (90^o - 70^o) ` and `sin (90^o - 70^o) = cos 70^o,` then`sin 20^o = cos 70^o = 0.2.`
The co-function identity give you `cos(Pi/2-x)=sinx`
Using degree measure that implies cos(90-x)=sinx, thus
cos(70)=cos(90-20)=sin(20)=0.2