# Math 30-1 - Trig - Unit circle and angles

Flashcards by Lauren Jatana, updated more than 1 year ago
 Created by Lauren Jatana over 5 years ago
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### Description

Trig - Unit circle and angles

## Resource summary

 Question Answer What 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) What 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) 176* to rads (exact and decimal) 176* x (pi/180) = 3.07 rads (always check the units are proper while using a "conversion factor") What is a good trick to convert radians (with pi in it) to degrees? e.g. Pi/4 Think of Pi as 180*. That means Pi/4 is 180/4 = 45* MEMORIZE: 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 What 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 What 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! What is the formula for arc length? a=r*theta What is ONE thing you should remember for arc length formula? THETA (or angle) is ALWAYS in radians. Always. What is tan, man? Tan is such a poser! Tan is actually sin/cos * (non alphabetical, s/c) Tan = sin/cos ... so If 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! 1. 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!) What is Tan, Sec, Csc, Cot? Tan = Cos/Sin Sec = 1/Cos Csc = 1/Sin Cot = 1/Tan = Sin/Cos (see first line) How 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. What 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? Use 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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