Pre-Calculus 12 Notes

By: Gen L.

Lesson 1: Radians

Right Triangle Trig

This is right angle trig.

• SOHCAHTOA

Reciprocity

Each trig ratio has a reciprocal:

Angles Units

Previously, we have measured angle size in degrees ().
Now, we'll measure them in radians .

1 Radian: the measure of the angle formed by an arc length equal to the radius.

• How big is this? Let's see:

Calculating 1 radian

How big is 1 radian?

.

Radians

• How many radian would fit halfway around a circle?
• Then, how many would fit around the circle?

Conversion

• First, you should be able to convert between radians and degrees.
• Where we start:

Degrees to Radians:

Conversion, cont.

Radians to Degrees:

Review

• Math 10: Right Angle Trig
• PC11: Triangle Trig Coordinate Trig
• PC12: Signed Coordinate Trig, Radians

Standard Position

• Angle that follows these rules:
  • Vertex at
  • Initial arm on -axis
  • direction

Co-terminal angles

Hope you like spirals!

• Angles w/ same terminal arm
• Smallest 've coterminal angle is the Principal.
• To find all angles:
  • or
  • or

Determining Arclength

• Determine the arclength of a circle w/ (no units means radians.)

• How about a general solution?

Measuring angles

There are 4 ways to measure angles:

1. Revolutions (rev) or
2. Degrees ()
   • mins & sec ()
3. Radians (rad, r, no units)
4. Gradians (grad), mostly used for construction

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