Question

Can someone give me the steps to solving this?

Answer 1

`\tan \theta = (8)/(15)`

Step by step explanation:

`\text{Given that,}\\\\~~~~~~~\sin \theta = (8)/(17)\\\\\implies \sin^2 \theta = (64)/(289)\\\\\implies 1-\cos^2 \theta = (64)/(289)\\\\\implies \cos^2 \theta = 1-(64)/(289)\\\\\implies \cos^2 \theta = (225)/(289)\\\\\implies \cos \theta =\pm\sqrt{(225)/(289)}\\\\\implies \cos \theta = \pm(15)/(17)`

`\text{In quadrant I, all ratios are positive, so,}~ \cos \theta = (15)/(17)\\\\\text{Now,}\\\\\tan \theta = (\sin \theta )/(\cos \theta)\\\\\\~~~~~~~~=\frac{\tfrac{8}{17}}{\tfrac{15}{17}}\\\\\\~~~~~~~~=(8)/(17) * (17)/(15)\\\\\\~~~~~~~=(8)/(15)`