If sin(θ)=2/7, and θ is in quadrant II, find cos(θ), sec(θ), csc(θ), tan(θ), cot(θ).

Question

If sin(θ)=2/7, and θ is in quadrant II, find cos(θ), sec(θ), csc(θ), tan(θ), cot(θ).

Answer 1

* |

| * | Use Pythagorean Theorem to find missing side.

| * 7 | 2² + x² = 7²

2 | * | 4 + x² = 49

| * | x² = 45

-------------|------------------------------------------------------------- x = root(45) = 3root(5)

- 3root(5) | cos(theta) = - 3root(5) / 7

| tan(theta) = - 2 / 3root(5)

| cot(theta) = - 3root(5) / 2

| sec(theta) = - 7 / 3root(5)

csc(theta) = 7/2

(some teachers want you to rationalize the denominator if it contains a root.)