Question

1. θ is a first quadrant angle in standard position and cos 1/(sqrt10)= . Find the exact value of sin .

2. feta is a second quadrant angle in standard position and tan(feta) -((sqrt5)/2) = . Find the exact value of cos(feta) .

3. θ is an angle in standard position with domain 0° <θ< 360° and cot θ -(24/7)= . Find all possible values of θ (accurate to 0.1° if necessary)

Answer 1

feta = β

Answer 2

1. draw a diagram. Legs are 1 and 3, hypotenuse is √10. If cosθ = 1/√10, sinθ = 3/√10

2. legs are √5 and 2, hypotenuse = 3. If tanθ = √5/2, cosθ = 2/3. In QII, cosθ = -2/3

3. legs are 7,24, hypotenuse =25
if cotθ < 0, θ is QII or QIV.

Arccot(24/7) = 16.26°, so

θ = 163.74° or 343.74°