MATH1110 Lecture Notes - Lecture 1: Unit Circle, Pythagorean Theorem, Jet Fuel
18 Jun 2018
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MATH1110: Mathematics 1
More functions I
1 Trigonometric Functions
Definition 1. The basic trigonometric functions are sin,cos and tan. These functions
are defined in terms of triangles sitting inside the unit circle. The unit circle is a circle
of radius 1 centred at the origin.
ø
(1,0)
(0,1)
(-1,0)
(0,-1)
sin(ø)
cos(ø)
øx
y
We usually measure the angle in radians. Radians measure the distance around the unit
circle from (1,0) on the positive x-axis to the point where the triangle touches the circle.
Therefore 2πradians equals 360 degrees, and all other angle conversions are proportional.
sin(φ) := the height of the triangle, multiplied by −1if the triangle sits below the x-axis.
cos(φ) := the width of the triangle, multiplied by −1if the triangle sits left of the y-axis.
tan(φ) := sin(φ)
cos(φ)is the ratio between the two.
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Document Summary
The basic trigonometric functions are sin, cos and tan. These functions are de ned in terms of triangles sitting inside the unit circle. The unit circle is a circle of radius 1 centred at the origin. y (0,1) sin( ) (-1,0) cos( ) x (1,0) (0,-1) Radians measure the distance around the unit circle from (1,0) on the positive x-axis to the point where the triangle touches the circle. Three of the following angles are equivalent to the angle 60 degrees and one is not. A large range of phenomena can be described using the trigonometric functions, because they model behaviour which is periodic. Any kind of wave in nature, the motion of a pendulum, the motion of the planets around the sun: these can all be described with various combinations of the trigonometric functions. We may use the de nition of the trigonometric functions to gure out their graphs.
