Unit+Circle

==CHECK FIRST LINE/GRAMMAR, PROVIDE AT LEAST 2 EXAMPLES solved through and unsolved with answers. The videos are good but do not give explicit examples. REFER TO THE FIRST PAGE OF THE REVIEW PACKET.==

Unit Circle by: Susan McGowan, Rachel Breslow, and Gabe Siegal Set 6

 * What is a Unit Circle?**

A unit circle a ... It is based on 360 degrees, or 2π in radians. Out of the 360 degrees it is divided into four quadrants. Quadrant I is 0 to 90 degrees and x and y are both positive. Quadrant II is 90 to 180 degrees and x is negative and y is positive. Quadrant III is 180 to 270 degrees and both x and y are negative. Lastly, Quadrant IV is 270 to 360 degrees and x is positive and y is negative.


 * Important Things to Remember**


 * y=sin
 * x=cos
 * y/x=tan
 * 1/y=csc
 * 1/x=sec
 * x/y=cot
 * use x²+y²=r²
 * to find the reference angle of an angle (x)
 * in Quadrant I x=reference angle
 * in Quadrant II use 180-x
 * in Quadrant III use x-180
 * in Quadrant IV 360-x
 * to convert degrees (x) to radians
 * (x)(π/180)
 * ex. (30°)(π/180)=π/6
 * to convert radian (x) to degrees
 * (x)(180/π)
 * ex. (π/6)(180/π)=30°


 * Common Mistakes**


 * Calculator set to degrees not radian or vice versa.
 * When trying to find reference angle using 90 or 270 instead of 180 and 360
 * Videos**
 * Videos**

Additional unit circle help: media type="youtube" key="6Qv_bPlQS8E" height="344" width="425" How to remember the unit circle: media type="youtube" key="cIVpemcoAlY" height="344" width="425" ex.1) If //θ// is a 2nd quadrant angle and tan//θ//= -¾, find the value of the other trig functions:
 * Practice Problems**

tan//θ =// sin//θ///cos//θ// x²+y²=r² //-//4²+3²=5² x=-4 y=3 r=5

sin//θ//=3/5 csc//θ//=5/3 cos//θ//=-4/5 sec//θ//=-5/4 tan//θ//=-3/4 cot//θ//=-4/3

ex.2) Express each of the following in terms of a reference angle.

cot285°:

since 285° is in the IV quadrant to find the reference angle you use 360-x. Substitute 'x' for 285. 360-285=75

since cot is //x///y and in quadrant IV x=positive and y=negative the reference angle will be negative.

cot285°= -(cot75°)