Math 30A   Arcs   Unit Circle   Sine/Cosine Transformations   Trigonometry Review   Prerequisite Skills

Unit Circle (radius = 1 unit) - Select 24 on both applets before printing.

What to Learn: Study the unit circle pattern of exact values for each function.

Help to Remember What to Learn

Interactive Activity

[cos x, sin x]

Linked Source - Ron Blond
 

For the unit circle, the trigonometry ratios for the reference angles in the first quadrant are shown below. We use 30o-60o-90o and 45o-45o-90o triangles to determine these ratios.

angle
sin
cos

tangent

sin

cos
0o
0
1
0
30o
1/2
45o
1
60o
1/2
90o
1
0
undefined

In the unit circle, the reference angles in the first quadrant are 0o, 30o, 45o, 60o and 90o.

The hypotenuse of the 30o-60o-90o and 45o-45o-90o triangle is 1 to match the hypotenuse of the right triangle in the unit circle.
 

The unit circle in the applet below is used to construct sine, cosine and tangent values from

0o < x < 360o (0 < x < 2π rad).

The blue/green radii outline the reference angle in quadrant 1 and the corresponding angles in quadrants 2-4. Note the radii are displayed in pairs to show the equivalent crest or trough locations on the graph.

 

Drag the blue data point on the unit circle clockwise to increase the size of the refence angle.

Linked Source - Ron Blond

Math 30A   Arcs   Unit Circle   Sine/Cosine Transformations   Trigonometry Review   Prerequisite Skills

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