Question

determine sin theta to three decimal places when tan theta=1/2 and theta is an angle in standard position

Answer 1

To find sin theta using the tan theta, firstly we should express the cot theta through the tan theta, using the trigonometric identity

$$tan θ*cotθ=1;$$

$$cotθ=1/tanθ=1/1/2=2;$$

Then we can use another trigonometrical feature:

$$sinθ=\sqrt{1/(1+cot^2θ)}=\sqrt{1/(1+2^2)}=$$

$$=\sqrt{1/(1+4)}=\sqrt{1/5}=1/\sqrt{5}=0.447$$