Angles and the Unit circle Chapter 13 Section 2 Angles and the Unit circle

Parts of an angle Terminal Side Vertex Initial Side

Standard Position Vertex is at the center Initial side is on the + x axis 700

Standard Position If terminal ray is in the II quadrant 300

Standard Position If terminal side is in the III quadrant 200

Standard Position If terminal side is in the IV quadrant 400

Find the measure of each angle 110 150 450

Negative Angle If you measure an angle counter clockwise you call can give the angle a negative degree -400

Co-Terminal measures A negative angle and + angle measure that describe the same angle are called Co- Terminal -400 and 320o are co-terminal

Find the Co Terminal Angle -350 -2000 -3000 -2820 1850 3300

Unit Circle A Circle with a radius of one unit centered on the origin (1,0) 1 unit

Unit Circle For angles in standard position we use the variable q to show we are talking about an angle ( q (1,0) 1 unit

For any point on the unit circle, we can find the coordinates by using the angle in standard position and the rule (cos(q) , sin(q)) (cos(300) , sin(300)) 300 (1,0) 1 unit

Cosine and Sine of 30-60-90 triangles 2 1

Cosine and Sine of 30-60-90 triangles 2 1 300

Cosine and Sine of 45-45-90 triangles 1 450 1

Make a 30-60-90 triangle and look at the coordinates For angles with a terminal side not in the 1st quadrant Make a 30-60-90 triangle and look at the coordinates (- , ) 1200 (1,0) 1 unit

Make a 30-60-90 triangle and look at the coordinates For angles with a terminal side not in the 1st quadrant use the rule QI (+,+) QII (-,+) QIII (-,-) QIV(+,-) Make a 30-60-90 triangle and look at the coordinates 2100 (1,0) 1 unit (- ,- )

For angles with a terminal side not in the 1st quadrant use the rule QI (+,+) QII (-,+) QIII (-,-) QIV(+,-) U Try 3000 (1,0) 1 unit ( ,- )

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