All the trig I need for AP Calculus AB
What I Need to Know from Trig
[the stuff I was supposed to have learned last year]
[By the way, you’ll need to be able to do this WITHOUT a calculator!]
Note: AP Calculus AB never uses degrees – only radians
0° = 0 90° = [pic]
30° = [pic] 180° = [pic] Opposite Hypotenuse
45° = [pic] 270° = [pic]
60° = [pic] 360° = 2[pic] Adjacent
In AP Calculus you should memorize the six trig function values above.
Right Triangle SOHCAHTOA
sin[pic] = [pic] cos[pic]= [pic] tan[pic] = [pic]
csc[pic] = [pic] sec[pic]=[pic] cot[pic] =[pic]
Circular Functions
(x,y) (cos[pic], sin[pic])
sin[pic] = [pic] csc[pic] = [pic] rr
cos[pic] = [pic] sec[pic] = [pic] ( -1, 0) (1, 0) (1, 0)
tan[pic]=[pic] cot[pic]=[pic]
1 radian [pic] 57.3°
[pic]1.57
3.14 6.28
The most important trig formula: sin2 θ + cos 2 θ ’ 1
from which we can derive other useful trig formulas.
(Divide all parts by sin2 θ) and we get 1 + cot2θ ’ csc2[pic]
(Divide all parts by cos2[pic]) and we get tan2[pic] + 1 = sec2[pic]
II I
S A
T C
III IV
Trig Graphs
[pic] [pic] [pic]
[pic] [pic] [pic]
Special Right Triangles
In the AP- world, the answer [pic] does not need to be rationalized (Hooray!). It is sometimes easier (at least for me) to recall trig values using triangles rather than using the unit circle.
[pic]
1 2 1 [pic] [pic] [pic][pic]
[pic] 1
Inverse trig functions
sin-1[pic] = arcsin[pic] ---- means the arc (or angle) whose sine is equal to some given value.
For example: sin-1[pic] = [pic] means [pic]
INVERSE FUNCTIONS ARE NOT RECIPROCALS!!!
What I Need to Know from Pre Calculus
Linear equations:
slope-intercept form: [pic]
point-slope form: [pic]
Parallel lines have equal slopes (except vertical lines which have undefined slopes)
Perpendicular lines have slopes whose product is –1 (opposite reciprocals)
slope = [pic]= [pic]
Distance formulas:
from point [pic] to [pic]: [pic]
from point [pic] to line[pic]: [pic]
Domain and Range: Interval Notation
−1≤ x ≤1 can be written as [ -1, 1] −1< x ................
................
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