FM - Further Pure 1 - 5) The t-formulae

Question 1

sin(θ), cos(θ) and tan(θ) when t = tan(θ/2)

Answer 1

• sin(θ) = (2t)/(1+t²)
• cos(θ) = (1-t²)/(1+t²)
• tan(θ) = (2t)/(1-t²)

Question 2

Triangle for t-formulae

Answer 2

• Right-angled triangle
• Acute angle of θ/2
• Opposite: t
• Adjacent: 1
• Hypotenuse: √(1+t²)

Question 3

Double-angle formula

Answer 3

• sin(2θ) = 2sin(θ)cos(θ)
• cos(2θ) = cos²(θ) - sin²(θ) = 2cos²(θ) - 1 = 1 - 2sin²(θ)
• tan(2θ) = (2tan(θ))/(1 - tan²(θ))