Question

What are the values of sin α and tan α, if:
cosα=0.6

Answer 1

Positive cosine is first or fourth quadrant. So we don't know the sign of the sine or the tangent.

Everybody's favorite right triangle is 3/4/5 and here we have

`\left(\frac 3 5 \right)^2 + \left(\frac 4 5 \right)^2 = 1`

So if

`\cos \alpha = 0.6 = \frac 3 5`

then

`\sin \alpha = \pm (4)/(5) = \pm 0.8`

and

`\tan \alpha = (\sin \alpha)/(\cos \alpha) = (\pm 0.8)/(0.6)=\pm \frac 4 3`