Answer
$$sin \space \theta = \frac{3}{10}$$ $$cos \space \theta = \frac{\sqrt {91}}{10}$$ $$tan \space \theta = \frac{3}{\sqrt {91}}$$ $$csc \space \theta = \frac{10}{3}$$ $$sec \space \theta = \frac{10}{\sqrt {91}}$$ $$cot \space \theta = \frac{\sqrt{91}}{3}$$
Work Step by Step
1. Find the last side value:
$$adjacent^2 + opposite^2 = hypotenuse^2$$ $$adjacent^2 + (3)^2 = (10)^2$$ $$adjacent^2 = 100 - 9 = 91$$ $$adjacent = \sqrt {91}$$
2. Find the trigonometric ratios:
$$sin \space \theta = \frac{opp.}{hyp.} = \frac{3}{10}$$ $$cos \space \theta = \frac{adj.}{hyp.} = \frac{\sqrt {91}}{10}$$ $$tan \space \theta = \frac{opp.}{adj.} = \frac{3}{\sqrt {91}}$$ $$csc \space \theta = \frac{hyp.}{opp.} = \frac{10}{3}$$ $$sec \space \theta = \frac{hyp.}{adj.} = \frac{10}{\sqrt {91}}$$ $$cot \space \theta = \frac{adj.}{opp.} = \frac{\sqrt{91}}{3}$$
