Unit Circle CALCAB
Convert to Degrees
Multiply 180/pi
Reference Angle
Smallest positive acute angle determined by x-axis
Express in terms of reference angle (acute)
1. Question: csc 300 deg 2. We find an acute angle from the graph, so it's 60 3. When looking at graph, it's in Q4 4. We use the acronym ASTC, and see that csc (which is actually sin) is only positive in Q1 or Q2, so the answer has to be a negative value 5. Last just write in csc 60 and add a negative to get -(csc 60) WHATEVER EXPRESSION YOU FOUND IT IN, LEAVE IT (sin as sin, csc as csc) Also, it could be its own reference angle
Find trig ratio for quadrantal angle
1. Question: csc pi/2 2. We know csc is sin, so find sin of pi/2 (90 deg) 3. The point at 90 deg is 0,1 4. We know sin is 1 5. Now it was csc so take reciprocal 6. 1/1 is the same as the reciprocal 7. So the answer is 1
30 60 90 Triangle
30 x 60 x√3 90 2x
45 45 90 Triangle
45 x 45 x 90 x√2
Quadrant Negative Helper
All Student Take Calculus A S T C Q1-All (pos) Q2-Sin (pos) Q3-Tan (pos) Q4-Cos (pos)
Degrees 180 Radians pi
Cos -1 Sin 0 Tan 0
Convert to Radians
Multiply pi/180
Find positive and negative coterminal angle
Number +or- 360
Standard Position
Positive Counterclockwise Negative Clockwise
X Y R ratios
Sin y/r Cos x/r Tan y/x Csc r/y Sec r/x Cot x/y
Degrees 45 Radians pi/4
Cos √2/2 Sin √2/2 Tan 1
Degrees 240 Radians 4pi/3
Cos -1/2 Sin -√3/2 Tan √3
Degrees 120 Radians 2pi/3
Cos -1/2 Sin √3/2 Tan -√3
Degrees 225 Radians 5pi/4
Cos -√2/2 Sin -√2/2 Tan 1
Degrees 135 Radians 3pi/4
Cos -√2/2 Sin √2/2 Tan -1
Degrees 210 Radians 7pi/6
Cos -√3/2 Sin -1/2 Tan √3/3
Degrees 150 Radians 5pi/6
Cos -√3/2 Sin 1/2 Tan -√3/3
Degrees 270 Radians 3pi/2
Cos 0 Sin -1 Tan undefined
Degrees 90 Radians pi/2
Cos 0 Sin 1 Tan undefined
Degrees 0 Radians 0
Cos 1 Sin 0 Tan 0
Degrees 360 Radians 2pi
Cos 1 Sin 0 Tan0
Degrees 300 Radians 5pi/3
Cos 1/2 Sin -√3/2 Tan -√3
Degrees 60 Radians pi/3
Cos 1/2 Sin √3/2 Tan √3
Degrees 315 Radians 7pi/4
Cos √2/2 Sin -√2/2 Tan -1
Degrees 330 Radians 11pi/6
Cos √3/2 Sin -1/2 Tan -√3/3
Degrees 30 Radians pi/6
Cos √3/2 Sin 1/2 Tan √3/3
Find exact value (possibly your hand, but here's the alternate option)
1. Question: sec 5pi 2. Get down to an acute angle by doing what you would do with coterminal degrees: subtract 360! Which is actually 2pi in radians 3. Next, you take your single pi, and realize that it's 180, so you look at the cos (which is sec) for 180 4. It is -1 so you take the reciprocal (which is also -1) and there's your answer.
Circumference of a Circle
2 * pi * r
Coterminal Angles
2 Angles in standard position that share a terminal side