Unit Circle CALCAB

Pataasin ang iyong marka sa homework at exams ngayon gamit ang Quizwiz!

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

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

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

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 45 Radians pi/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

Convert to Degrees

Multiply 180/pi

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

Reference Angle

Smallest positive acute angle determined by x-axis


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