Trigonometry functions

Question

Find the six trigonometric functions of θ.

1. P(1,1)
2. P(4, -3)

Answer 1

1) P(1,1) is on 45° (π/4) ray from origin, so the Unit Circle provides the sin and cos values: sin θ = √2 /2, cos θ = √2 /2, tan θ = 1, csc θ = 1/sin θ, sec θ = 1/cos θ, cot θ = 1/tan θ (you can provide these values).

2) P(4,-3) defines a 3-4-5 right triangle in the 4th quadrant; from x=4, drop down -3 and produce the hypotenuse from the origin to point P. sin θ = -3/5, cos θ = 4/5, tan θ = -3/4, csc θ, sec θ, cot θ as above.