Question

Consider ∠A such that cos A = 12/13.

a) In which quadrant(s) is this angle? Explain.

b) If the sine of the angle is negative, in which quadrant is the angle? Explain.

c) Sketch a diagram to represent the angle in standard position, given that the condition in part b) is true.

d) Find the coordinates of a point on the terminal arm of the angle.

e) Write exact expressions for the other two primary trigonometric ratios for the angle.

Answer 1

A)

Using the unit circle, for the cos function to be positive, angle A must lie in either quadrant I or quadrant IV

B)

Using the unit circle, If the sine is negative, angle A must lie in either quadrant III or quadrant IV. Since we know that the cosine is positive, this only leaves quadrant IV

D)

cos = adj/hyp

Using Pythagorean theorem,

$12^{2} +b^{2} = 13^{2}$

b = ±5 (we know its -5 since we know sinA is negative)

this means that the x coord is 12, and the y coord is -5

any proportion of these two numbers would work as an answer

e.g. (12, -5), (24,-10),  (12/13, -5/13), are all valid answers

E)

sinA = opp/hyp

sinA = -5/13

tanA = opp/adj

tanA = -5/12