Cogito
Integrated Math 3 · Chapter 5 · Lesson 1
The Unit Circle and Radians
Trigonometry beyond the triangle.
12 problems · about 21 minutes · F-TF.A.1, F-TF.A.2
What this lesson teaches
The student defines sine and cosine on the unit circle and converts between degrees and radians.
- On the unit circle the terminal point is (cos θ, sin θ).
- The reference angle gives the size; the quadrant gives the sign.
- A full turn is 2π radians, and the functions repeat every turn.
Warm Up
Straightforward practice. Get the method working first.
5 problemsWhat is the reference angle for 200°, in degrees?
Answer 20
Why 20°.
What decides the sign of a trigonometric value?
Answer The quadrant, through the signs of the coordinates.
Why The quadrant.
What is sin 90°?
Answer 1
Why The point is (0, 1).
What is cos 180°?
Answer -1
Why The point is (−1, 0).
Reference angle for 210°, in degrees?
Answer 30
Why 210 − 180.
Build It Up
The same ideas with more to keep track of.
3 problemssin 210° as a decimal?
Answer -0.5
Why Reference 30°, quadrant III.
How many degrees is 2π radians?
Answer 360
Why A full turn.
Reference angle for 300°, in degrees?
Answer 60
Why 360 − 300.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsIn which quadrants is sine positive?
Answer Quadrant I; Quadrant II
Why Sine follows y, which is positive on the upper half.
cos 300° as a decimal?
Answer 0.5
Why Reference 60°, quadrant IV.
The Reference: What is the reference angle for 150°, in degrees?
Answer 30 degrees
Why 30°.
The Conversion: How many degrees is π radians?
Answer 180 degrees
Why 180°.