Mathematics

Problem

Consider the trigonometric functions defined on the unit circle. a. (a) Explain, with the help of the unit-circle definition, why the x-coordinate of a point at an angle

x

equals the y-coordinate of a point at an angle

\dfrac{\pi}{2}-x

. b. (b) Hence justify the relation

\cos x = \sin\left(\dfrac{\pi}{2}-x\right)

for all real

x

. c. (c) Describe how the above relation affects the symmetry of the graphs of

y=\sin x

and

y=\cos x

Browse the problem library