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Math 30-1 - Trig - Unit circle and angles
Karten in diesem Stapel (16)
- 1What is the difference between degrees, radians and revolutions? Make up an angle and convert it to all three types.i.e. 1/3 revolution, would be 1/3rd of 360*, which would be 120*, and 120/180 = 2/3 Pi. ( 180 is PI, so I ask myself, how many Pi's is 120? OR... alternatively a full circle is 2Pi, so I can take 1/3rd of 2Pi)
- 2What is the conversion factor for converting degrees to radians? *How can you "check" that you remembered the correct conversion factor?Conversion factor for degrees to rads:
Pi/180
You HAVE to check units, top and bottoms cross out, then check right hand side (RHS) units is equal to left hand side. (LHS) - 3176* to rads (exact and decimal)176* x (pi/180) = 3.07 rads
(always check the units are proper while using a "conversion factor") - 4What is a good trick to convert radians (with pi in it) to degrees? e.g. Pi/4Think of Pi as 180*.
That means Pi/4 is 180/4 = 45* - 5MEMORIZE: What is EXACT sin30*, sin45*, sin60*? I will use to build unit circle, yes I will!* all denominators are 2!
* all numerators are √1, √2 or √3
* sin 30* = √1/2,
sin 45* = √2/2
sin 60* = √3/2
* cos is just opposite! √3,√2,√1 - 6What are the steps to building the unit circle? How far can you get without checking?1. Draw a circle
2. Label the axis with angles, and the 3 main angles
3. label x (horizontal) and y (vertical) value of each "triangle" in the circle (memorize)
* all denominators are 2, tops are either √1 √2 or √3 - 7What do the "coordinates" of the unit circle mean? (in what specific order?) Can you confirm?(x,y) = (cos, sin)
(Alphabetical)
If I make a triangle, the "O" is vertical which would mean "y" coordinate. Opposite (o) relates to SOH, or Sin. SOOOOO y relates to sin. I feel confident! - 8What is the formula for arc length?a=r*theta
- 9What is ONE thing you should remember for arc length formula?THETA (or angle) is ALWAYS in radians. Always.
- 10What is tan, man? Tan is such a poser!Tan is actually sin/cos
* (non alphabetical, s/c)
Tan = sin/cos ... so - 11If you know what Tan really is, what is Tan(Pi/6)? can you check? are you confident?Pi/6 is really... 180/6 = 30*
Tan 30, I have to know sin 30, and cos 30...
Think back to what you memorized.
tan30 = sin30/cos30 so..
tan30 = (1/2) / (√3 /2) ... fraction time! - 121. Unit circle (x,y) is... 2. Tan really is... ?/? 3. Sin30* vs. Cos30*1. Unit circle is cos, sin (alphabetical)
2. tan = sin/cos (not alphabetical)
3. sin builds √1,√2,√3 and cos builds √3.√2,√1...
so sin30 = 1/2 and cos30= √3/1
(sin in my favorite, it's first in SOH CAH TOA, and is 1,2,3 order!) - 13What is Tan, Sec, Csc, Cot?Tan = Cos/Sin
Sec = 1/Cos
Csc = 1/Sin
Cot = 1/Tan = Sin/Cos (see first line) - 14How do I know NPV's? of a function?If it has any denominator (as per usual), but if it has Tan, Sec, Csc, Cot too! They have embedded denominator in their definition.
- 15What is a reference angle?1. An angle that is less than 90* always
2. If you put the angle on the unit circle, or a graph - it will ALWAYS be measured from the X-axis
3. It is the one that could be put into a triangle... i.e can you put 130* into a triangle? - 16Use the reference angle to calculate Cos(120*)...1. Draw 120* on the axis
2. The closest angle to x-axis is 60* (in QII)
3. So we are really calculating Cos(60*)
4. Cos(60*) = 1/2
5. In QII - Cos is negative, so -1/2 is the answer
6. CHECK WITH CALCULATOR
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- Trig - Unit circle and angles
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- Lauren Jatana
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