Unit Circle and Radian Defining
Collection of best activities to Explore Unit Circle and Defining Radius
Table of Contents
- Understand Unit Circle
- Copy of Exact values on the unit circle (degrees)
- Radian Illustrator
- Radian Units
- 1 Radian: Clear Definition
- Arc length: Quick Investigation
- Visualizing Radians and Arc Length
- Radian and Degree
- Convert Radians with Degrees
- Explore Converting Between Degrees and Radians
- DEG to RAD and RAD to DEG: Question Generator
- Unit Circle with Radians
- Quiz
Copy of Exact values on the unit circle (degrees)
Exact values around the unit circle.
Explore Unit Circle
Answer these questions
Q1
Use the Applet to Drag the Green point on the circle to make an angle of 120 degrees and write the reference angle for 120 degrees and Enter the Value of [math]sin\left(120^o\right)[/math]
Q2
Use the Applet to Drag the Green point on the circle to make an angle of 210 degrees and write the reference angle for 210 degrees and Enter the Value of [math]cos\left(210^o\right)[/math]
Q3
Use the Applet to Drag the Green point on the circle to make an angle of 240 degrees and write the reference angle for 240 degrees and Enter the Value of [math]tan\left(240^o\right)[/math]. Describe why the value is positive or negative? (tangent is ratio of sine and cosine)
Q4. Drag the Point to the angle 330 degrees and answer these question
a. What are the other angles which can give the value the same as of sin(330)?[br]b. What are the other angles which can give the value the negative of sin(330)?
Q5. Describe these in terms of values of sine, cosine and tangent
a)What is the general relationship between the values (with sine and cosine) of two angles if they differ by 360 degrees, Like sin(30) and sin(390).[br][br]b)What is the general relationship between the values of two angles if they differ by 180 degrees, Like [br]cos(120) and cos(300) or 30 and 210.[br][br]c) What is the general relationship between the values of two angles if they differ by 90 degrees, Like 60 and 150 or 45 and 135.
Convert Radians with Degrees
A "radian" is an alternative way of measuring an angle. It was developed for a particular purpose that you will soon see is quite useful. So what is a radian?[br][br]If you place the radius of a circle on the outside of a circle, the central angle created with the arc is called "1 radian." For each radius place on the outside of the circle you increase the angle of the central angle in radians. This is an alternative way of measuring an angle using the radius of a circle. The unit of measurement is called a "radian."[br][br]It appears that the angle in radians around the circle is a bit more than 6 radians.
Thanks to Mr. Landry Deering Math [url]http://www.deeringmath.com/videos/precalculus/radian/part1/index.html[/url]