Homework SourseA label the coordinates that you would be at if you walked f
A) label the coordinates that you would be at if you walked from (1,0) a distance of t units around the unit circle.
B) on the unit circle, mark the arcs of length (t-pi/2) and (t+pi), the triangles that we can associate with them, and then label each point in terms of a.
C) find the value of the following given the information above
i) csc(t-pi/2)
ii) tan(t+pi)
iii) sin^2(t+pi) + cos^2(t+pi)
Solution
As per the diagram :
i) csc( t- pi/2) = 1/sin(t-pi/2)
sin( t -pi/2) = - sqrt(1- a^2)/1
so, csc( t- pi/2) = - 1/sqrt( 1- a^2)
ii) tan(t +pi) = tant = a/sqrt(1- a^2)
iii) sin^2(t+pi) + cos^2(t+pi) = 1
