Question

Determine the values of sin, cos, tan, csc, sec and cot at (-3, -3) on the terminal arm of an angle in standard position

2. If cos θ = 2/3 and 270° < θ < 360° then determine the exact value of 1/cot

Answer 1

1. tanAr = Y/X = =-3 / -3 = 1.00,
Ar = 45deg. = Ref. angle.

A is in 3rd Quadrant.
A = 180 + 45 = 225deg.

sin(225)= -0.7071,

cos(225) = -0.7071,

tan(225) = 1.00,

csc(225) = 1/sin(225) =

sec(225) =

cot(225)

You can finish it.

2. Theta is bet. 270 and 360deg.

Given: cos(theta) = 2/3 = X/r.

X^2 + Y^2 = r^2,
2^2 + Y^2 = 3^2,
4 + Y^2 = 9,
Y^2 = 9 - 4 = 5,
Y = sqrt(5).

1/cot(theta) = tan(theta),
1/cot(theta) = Y/X = sqrt(5) / 2.