Embedded Files
Objectives:
- Learn the Unit Circle pattern
- Find exact trig values
- Convert radians into degrees
Key Concepts:
- Radians
- Degrees
- Unit Circle
- Degrees
- Angles
- QRS
Lesson 4.2: Learn the Unit Circle!
In this lesson, we will learn how to construct the unit circle by using a pattern. We will slowly build up the unit circle, so you can know it by heart and not have to memorize it! This is the end result:
First Step: Start labeling the circle on the grid with the specific angles. If there is a big gap between the x-axis or y-axis, then it means the angles increase by 30 degrees, if the lines are closer to each other, then it means the angles increase by 15 degrees.
Second Step: Finish labeling all of the angles on the unit circle with the rule stated above. Another way of solving for the angle just in case you get confused is that once you try labeling the angles on the circle, you subtract the reference angle from 180 to get angle in the second quadrant. In the third quadrant, you add the reference angle to 180. In the fourth quadrant, you subtract it from 360 since you are almost at a full circle. The reference angle of any angle on the unit circle, is a factor of the other. For example, the patterns go lime this: 0-180, 30-150-210-330, 45-135-225-315, 60-120-240-300, and 90-270.
Third Step: Label the unit circle with the radians. A radian is a fraction of a circle, their size is dependent of the arc length. To find the radian, divide the length of the arc by the radius of the circle. This is how you convert degrees into radians:
On the unit circle, you have to follow a specific pattern that you will most likely have to memorize. This is what it will look like:
Fourth step: One you have the part above done, you use the technique taught in 4.1 to solve for the value of the reference angle of Cosine, Sine, and Tangent across the unit circle.
You do that for the rest of the angles that follow. The values are the same across the circle for each degree measure that has the same reference angle.
Lastly, you change the signs of the values by using All Students Take Calculus.
If you are still confused, please watch this video:
End Result:
SAT and ACT testing:
This can be used to determine where an angle opens in the coordinate plane. (A radian is another way of measuring an angle, like a degree. There are a total of 2π radians in a circle.) If you’re told on the test that an angle is between π and 3π/2, for example, you know that the angle opens in the third quadrant.
Those are the principles you need to know! Master them, and you’ll be an ACT and SAT trigonometry expert in no time!
Google Sites
Report abuse