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What is Unit Circle?
What is Unit Circle?
The circle that has
center in the origin of the coordinate plane
radius 1 unit
counterclockwise sense of movement is considered the positive sense of movement
(clockwise sense is the negative sense: by example, the GIF above is moving clockwise, in the negative sense)
Why Unit Circle?
Why Unit Circle?
any angle (degrees or radians) can be represented through a point on unit circle
the sine and cosine of the angle can be easily seen using the unit circle, the x-axis (cosine) and the y-axis (sine)
Quadrants
Quadrants
4 quadrants (counterclockwise)
What are Radians?
What are Radians?
Radians (real numbers) vs Degrees (usual measure for angles)
Recall SOH CAH TOA
Let's see how SOH & CAH look on Unit Circle. Click on the image below.
Defining SIN & COS for extended angles
Defining SIN & COS for extended angles
Click on the image below to understand how sine and cosine for an extended angle are defined.
Extended angle = angle that has its measure any number of degrees or radians: positive, negative (lesser or greater than 180 degrees).
1st image: what 'theta' represents (the measure of the arc and central angle and also the length of the arc because the radius of Unit Circle is 1)
2nd image: naming the point P that represents the position of 'theta' on the unit circle
3rd image: look at the regular coordinates of point P. So, on x-axis is COS of 'theta', on y-axis is SIN of 'theta'. Period.
Let's summarize ....
To keep in mind the values of sine and cosine of the main angles on the 1st quadrant, analyze the carousel below. Click on the image to see how sine and cosine are working on unit circle.
So, according to all above, we can recall from Math 2 the values of sine and cosine of the main angles on the 1st quadrant (Math 2) ...
Now, it's time to infer the values of sine and cosine of the main angles of all 4 quadrants ...
Now, it's time to infer the values of sine and cosine of the main angles of all 4 quadrants ...
CHECK FOR UNDERSTANDING
CHECK FOR UNDERSTANDING
(Click 2nd time on the figure to check your answer!)
1. What is the value of cos x when x = 150 degrees?
2. What is the value of sin x when x = 240 degrees?
If you need more more, click on the pink button above.
If you think you got it, click on the pink button below for assignment.
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