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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