TRIGONOMETRY Accel Precalc Unit 5 Introduction to Trigonometry

TRIGONOMETRY

Accel Precalc Unit #5: Introduction to Trigonometry Lesson 1: Sketching Angles EQ: How do you sketch an angle in standard position whose measure is in degrees, pi radians, or decimal degrees?

RECALL: Identify all key parts of the rectangular coordinate plane. y-axis Quad II x-axis Quad I origin Quad III Quad IV

New Terms: Variables we will use for naming angles in Trig: theta alpha beta gamma

q. Angle Measures on the Axes: Degree Measure Radian Measure

Decimal Radian Measure:

Angles--Drawn Standard Position initialinray is on x axis; terminal ray may be drawn in a quadrant or on an axis; measure is made from initial ray to terminal ray

Positive Angles Drawn in Standard Position --- counter-clockwise direction from x axis; use an arrow to show direction and number of rotations (if necessary).

Negative Angles Drawn In Standard Position --- clockwise direction from x axis; use an arrow to show direction and number of rotation (if necessary).

Full Rotation vs What is one rotation through the coordinate plane? one rotation = 360˚ How to Sketch Angles: 54° = 180˚ 320°

-225° -120°

Sketch these angles in standard position.

Day 36 Agenda: Quiz #7 --- 30 minutes

Reference Angles --- positive acute angles; measured from the x axis

OMIT THIS IN YOUR NOTES

State the reference angle for Ex #1 – 5. 7. 10. 25˚ 8. 65˚ 11. 0. 28 9.

Coterminal Angles --- have same terminal ray, but different angle measure; infinitely many coterminal angles to one angle.

Find a positive and negative coterminal angle for each. 37˚+360˚= 397˚ -42˚+360˚= 318˚ 37˚- 360˚= -323˚ -42˚- 360˚= -402˚

RECALL: Complementary Angles --- sum of two angles is 90˚ Supplementary Angles --- sum of two angles is 180˚

DOES NOT EXIST

NEITHER EXISTS

Assignment: textbook p. 291 #5 – 21 odd, 27 – 41 odd