Math 201
Trigonometry Name:
This sheet is to help remind you of all the wonderful properties of trigonometric functions
(1) Recall that the unit circle consists of points in the plane, (x, y) such that the distance from
the origin is one. Use the Pythagorean theorem to express this statement about distance
as an equation with xand y.
x2+y2= 1
(2) One way to define sin(t) and cos(t) is as follows, pick a point on the unit circle (x, y). If the
angle between the positive x-axis and the line from the origin to this point is tthen define
cos(t) to be xand sin(t) to be y. Draw the first quadrant of the unit circle and label cos(t)
and sin(t) for t= 0, π/6, π/4, π /3, π/2. Using these angle and reflections of them you can
find the values of sin(t) and cos(t) for all multiples of these angles.
(3) What identity with sine and cosine does part one give us?
sin2(t) + cos2(t)=1
(4) The measure of angle we are using is radians. These are setup so that on the unit circle an
angle of one radian gives an arc length of one. In general the arc length is the radius times
the angle in radians. What is the arc length of half of a circle of radius 99?
(radius)(angle) = 99π
(5) Use your calculator to sketch a graph of sine and cosine over the domain −2πto 2π.
(6) The amplitude is the distance between the minimum and maximum values. What is the
amplitude of sin(t)? What would you need to do to triple the amplitude? (Hint: Think
about the shifts etc. from 1.3.)
The amplitude is2.
Multiply the function by 3, for example 3 sin(t).
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