Question

If cos theta is equal to -7/25 and theta (180°;360°) what is the value of 14 tan theta ​

Answer 1

`14 tan\theta = -48`

Explanation:

`cos \theta = (-7)/(25)\\\\cos^2 \theta = (49)/(625)\\\\sin^2 \theta = 1 - cos^2 \theta\\\\`

`=1 - (49)/(625)\\\\=(625-49)/(625)\\\\=(576)/(625)\\\\`

`sin \theta = \sqrt{(576)/(625)} = (24)/(25)`

`tan \theta = (sin \theta)/(cos \theta)`

`=((24)/(25))/((-7)/(25))\\\\=(24)/(25) * (25)/(-7)\\\\=(-24)/(7)`

`14 tan \theta = 14 * (-24)/(7) = 2 * -24 = -48`