Cogito
Trigonometry · Chapter 2 · Lesson 1
The Unit Circle
The same ratios, freed from the triangle.
10 problems · about 21 minutes · F-TF.A.1, F-TF.A.2, F-TF.A.3
What this lesson teaches
The student defines sine and cosine as coordinates on the unit circle and works in radians.
- On the unit circle, cosine is the x-coordinate and sine is the y-coordinate.
- That definition works for every angle, not just acute ones.
- A radian is the angle whose arc equals the radius; a full turn is 2π.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
2 problemsReview — Special Right Triangles: In a 30-60-90 triangle, the hypotenuse is 20. What is the short leg?
Answer 10
Why 10.
Review — The Reciprocal Ratios: Which ratio is the reciprocal of cosine?
Answer Secant.
Why Secant.
Warm Up
Straightforward practice. Get the method working first.
4 problemsWhat is sin 270°?
Answer -1
Why −1.
On the unit circle, what is the cosine of an angle?
Answer The x-coordinate of the terminal point.
Why Cosine is x, sine is y.
What is cos 0°?
Answer 1
Why The point is (1, 0).
What is sin 0°?
Answer 0
Why The y-coordinate.
Build It Up
The same ideas with more to keep track of.
2 problemsHow many degrees is 2π radians?
Answer 360
Why A full turn.
What is cos 180°?
Answer -1
Why The point is (−1, 0).
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Right Angle: What is sin 90°?
Answer 1
Why 1.
The Radians: How many degrees is π radians?
Answer 180 degrees
Why 180°.