given cosθ = - 4/5, 90° ≤ θ ≤ 180° and sin β = - 4/11, 270° ≤ β ≤ 360°

Question

a) Sketch a diagram for each angle, showing all important information.

b) Evaluate the expression; tan^2 β - sin^2 θ. answer in simplest exact form.

Answer 1

a) Later

b) Since,

cosθ = -4/5, 90° ≤ θ ≤ 180°

base, b = -4

hypotenuse, h = 5

So perpendicular, p = 3  using pythagoras theorem

Therefore, sinθ = 3/5 => sin^2 θ = 9/25   --------------------(1)

Again, sin β = - 4/11, 270° ≤ β ≤ 360°

So, p = -4, h = 11

b =  √{11^2 - (-4)^2} = √105

so, tanβ = -4/√105 => tan^2 β = 16/105  ------------------(2)

Using (1) and (2):

tan^2 β - sin^2 θ = 16/105 - 9/25  = -109/525