Question

Find the values of cosΘ and tanΘ, given that sinΘ = 8/9 and Θ is in quadrant I

Answer 1

`sin^2 \alpha +cos^2 \alpha =1\ \ \ and\ \ \ tan \alpha = \frac{\big{sin \alpha }}{\big{cos \alpha }} \\\\sin \alpha = (8)/(9)\\\\ \Rightarrow\ \ \ ((8)/(9))^2+cos^2 \alpha =1\ \ \ \Rightarrow\ \ \ cos^2 \alpha =1- (64)/(81) \ \ \ \Rightarrow\ \ \ cos^2 \alpha = (17)/(81) \\\\ \alpha \ \in\ (0^0;90^0)\ \ \ \Rightarrow\ \ \ cos \alpha >0\ \ \ \Rightarrow\ \ \ cos \alpha = ( √(17) )/(9) \\\\`


`tan \alpha = (8)/(9): ( √(17) )/(9) =(8)/(9)\cdot (9)/(√(17))= (8)/(√(17))= (8\cdot √(17))/(√(17)\cdot √(17))=(8\cdot √(17))/(17)`