A curve on a light rail track is an arc of a circle of length 300m and the straight line joining the two ends of the curve is 270m long.
a) show that, if the arc subtends an angle of 2x(degrees) at the center of the circle, x is a solution of the equations
sin x(degrees) = (pi*x)/200
b) solve, correct to 2 d.p., the equation for x
Name:
Anonymous2008-12-14 10:07
OP here ty ty - as for response 2 - i get the cosine rule usuage but what's Taylor expanding and bisection search?
NEW questions:
Let sec x = b where x - [pi/2, pi]. Find, in terms of x, two values of x in the range [-pi, pi] which satisfy each of the following equations:
a. sec x = -b
b. cosec x = b
normally can do these questions but this one makes it really confusing as the quadrant SHOULD be positive but it's negative.
Let tan x = b where x - [pi, 3pi/2]. Find, in terms of x, two values of x in the range [0, 2pi] which satisfy each of the following equations:
a. sec x = -c
b. cot x = c
Answers in the book (incase they're wrong) are:
1st q: a. pi - x, x - pi
b. pi/2 - x, x - 3pi/2
2nd q: a. 2pi - x, 3pi - x (3pi!?)
b. 3pi/2 - x, 5pi/2 - x
I got the first part of the first question but have no idea what method the answers are using