Question

When a pilot banks an aircraft moving at a speed, v, in metres per second, at an angle a, the radius of the turn that results is given by the formula:

r = v^2/g * tan(pi/2 - a)

where g is the accelatation due to gravity, or 9.8 m/s^2.
Use an appropriate equivalent trigonometric expression to show that this formula can be simplified to:

r= v^2 / (g*tana)

Answer 1

pi/2-a and a are complementary angles.

the trig ratio of any angle is the co-ratio of the complement of that angle.

e.g. sin 70 = cos 20
sec 25 = csc 65
and tan (pi/2 - a) = cot a

so
r = v^2/g * tan(pi/2 - a)
= v^2/g * cot a
= v^2/g * 1/tan a
= v^2/(g*tan a)

Answer 2

explain why tan 60degree=root3.