Theory question 109
Trigonometry(a) Simplify: 1/(1 − cos θ) + 1/(1 + cos θ) and leave the answer in terms of sin θ.
(b) Find the equation of the line joining the stationary points of y = x2(x − 3) and the distance between them.
Show the model answer
Model answer
(a) (1 + cos θ + 1 − cos θ)/(1 − cos²θ) = 2/sin²θ.
(b) y = x³ − 3x²; dy/dx = 3x² − 6x = 0 at x = 0 and 2. Points (0, 0) and (2, −4).
Line: y = −2x. Distance = √(4 + 16) = 2√5 ≈ 4.47.
Explanation
1 − cos²θ = sin²θ.