if cos theta = 0.3090, which of the following represents approximate values of sin thetha for 0 degrees <90 degrees? A. sin thetha =0.9511;tan theta = 0.3249 B.sin thetha =0.9511 ;tan thetha =3.0780 C. sin thetha 3.2362 ; tan thetha=0.0955D. sin thetha = 3.2362;tan thetha=10.4731

In this question, the given value is[tex] cos \theta = 0.3090 [/tex]And we have to find the value of sin theta and tan theta where theta is in first quadrant .And in first quadrant, all are positive .Now we use the formula, which is[tex] sin \theta = \sqrt{1-cos^2 \theta} = \sqrt{1 - 0.3090^2} = 0.9511 [/tex]And tan theta is the ratio of sin theta and cos theta, that is[tex] tan \theta = \frac{sin \theta}{ cos \theta} = \frac{0.9511}{0.3090} =3.078 [/tex]So the correct option is B .