Answer:
L = ∫₀²ᵖⁱ √((1 − sin t)² + (1 − cos t)²) dt
Step-by-step explanation:
Arc length of a parametric curve is:
L = ∫ₐᵇ √((dx/dt)² + (dy/dt)²) dt
x = t + cos t, dx/dt = 1 − sin t
y = t − sin t, dy/dt = 1 − cos t
L = ∫₀²ᵖⁱ √((1 − sin t)² + (1 − cos t)²) dt
Or, if you wish to simplify:
L = ∫₀²ᵖⁱ √(1 − 2 sin t + sin²t + 1 − 2 cos t + cos²t) dt
L = ∫₀²ᵖⁱ √(3 − 2 sin t − 2 cos t) dt
Answer:
Step-by-step explanation:
You know two sides and the angle between them. Use the Law of Cosines to find the third side.
q = √(p²+r²-2pr·cosQ) ≅ 8.533 units
Use Heron's formula to find area
semi-perimeter s = (p+q+r)/2 ≅ 10.317 units
area = √(s(s-p)(s-q)(s-r)) ≅ 16.3 units²
Answer:
90º
Step-by-step explanation:
just look at where 31º on the right lines up with the value on the left (aka around 90º)
