Question

if sin theta =1/3, calculate tan theta

Answer 1

Imagine a rectangle triangle, that the hypotenuse is 3 and one side is 1, using the Pythagorean theorem you'll find the other side.\[h^2=a^2+y^2\]\[3^2=1^2+y^2\]\[y^2=8\]\[y=2\sqrt{2}\]Then\[tan(\theta)=\frac{a}{y}\]the answer is:\[tan(\theta)=\frac{1}{2\sqrt{2}}=\frac{\sqrt{2}}{4}\]