Trigonometry

Solutions

Problem Set #2

1. Given are the three sides of a right triangle. If θ denotes the angle between the first side given and the hypotenuse, sketch the triangle and determine sin(θ), cos(θ), and tan(θ). Leave your answer in fraction form

a) 8,6, 10 sinθ =6/10 cosθ = 8/10 tanθ = 6/8

b) 2, 3, √13 sinθ =3/√13 cosθ = 2/√13 tanθ = 3/2

c) 5,5, √50 sinθ =1/√2 cosθ = 1/√2 tanθ = 1

(this is an isosceles triangle…both angles are 45 degrees)

d) 12,5,13 sinθ =5/13 cosθ = 12/13 tanθ = 5/12

2. Given are the two legs of a right triangle. . If θ denotes the angle between the first side given and the hypotenuse, sketch the triangle and determine sin(θ), cos(θ), and tan(θ). Leave your answer in fraction form

a) 2,5 h = √29 cos θ = 2/√29 sin θ = 5/√29 tan θ = 5/2

b) 1,4 h = √17 cos θ = 1/√17 sin θ = 4/√17 tan θ = 4

c) 15, 36 h=39 cos θ = 15/39 sin θ = 36/39 tan θ = 36/15

d) 21,20 h=29 cos θ = 21/29 sin θ = 20/29 tan θ = 20/21

e) 3, 3 h=3√2 cos θ = 1/√2 sin θ = 1/√2 tan θ = 1 (isosceles… 45 degrees)

3) In each case, cos(θ) is given. Deduce as much additional information from this as you can. Feel free to use a calculator

a) .3 θ = 72.54° so sin(θ)=.954

b) .5 θ = 60° so sin(θ)=.866

c) .866 θ = 30° so sin θ = 1/2

d) .81 θ = 35.9° so sin(θ)=.586