4.3: Circular Trigonometry February 4, 2013

Warm-up a)Find the remaining sides of the triangle if i.x = 5 ii.r = 1

Learning Targets

Standard Position Angles Vertex Initial Side Terminal Side Cartesian Plane / coordinate system / coordinate plane

Negative Angles

Coterminal Angles: Angles that have the same terminal side and the same initial side.

Coterminal Angles

How many coterminal angles are there to a given angle?

Example a)Find cos(30 ○ ) b)Find cos(150 ○ ) c)Find cos(210 ○ ) d)Find cos(300 ○ )

Reference Triangles A reference triangle is used to evaluate trig functions for non-acute angles. A reference triangle always has the x-axis as one side (never the y-axis). Which is the reference triangle? A B

When are the functions positive?

Re-Defining Sin, Cos, Tan If t is an angle on the unit circle, then:

The Unit Circle: A circle with radius = 1

Quadrantal Angle

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Example Find tan(300 ○ )

Example