Evaluating Trigonometric Functions for an Angle in the Coordinate Plane (6.3.1)

Question 1

• If (x, y) is a point on the terminal side of an angle θ, then
sinθ = y/r, cosθ = x/r, tanθ = y/x, cscθ = r/y, secθ = r/x, and cotθ = x/y, where r=sqrt(x^2 + y^2).

Answer 1

• If (x, y) is a point on the terminal side of an angle θ, then
sinθ = y/r, cosθ = x/r, tanθ = y/x, cscθ = r/y, secθ = r/x, and cotθ = x/y, where r=sqrt(x^2 + y^2).

Question 2

• For angles in quadrant I, All trigonometric functions are positive.
For angles in quadrant II, only Sine and its recipricocal function, cosecant, are positive.
For angles in quadrant III, only Tangent and its recipricocal function, cotangent, are positive.
For angles in quadrant IV, only Cosine and its recipricocal function, secant, are positive.
You can remember this with the saying “All Students Take Calculus.”

Answer 2

• For angles in quadrant I, All trigonometric functions are positive.
For angles in quadrant II, only Sine and its recipricocal function, cosecant, are positive.
For angles in quadrant III, only Tangent and its recipricocal function, cotangent, are positive.
For angles in quadrant IV, only Cosine and its recipricocal function, secant, are positive.
You can remember this with the saying “All Students Take Calculus.”