Trigonometric Formulas
This
is a list of the most common formulas that you should know, not only for the
exam, but just in general as you take calculus and beyond.
1st
Quadrant Measures:
|
|
radians |
|
|
|
|
0 |
0 |
0 |
1 |
0 |
|
30° |
|
|
|
|
|
45° |
|
|
|
1 |
|
60° |
|
|
|
|
|
90° |
|
1 |
0 |
N/A |
Also, be able to draw accurate
graphs of sin and cos.
Conversions
from other quadrants to 1st quadrant:
Q2
to Q1: p - q; Q3
to Q1: q - p; Q4
to Q1: 2p - q.
If
you forget these, draw a circle and use symmetry and common sense.
Signs
in other quadrants:
A
mnemonic: "All Students
Take Calculus". A = all are + in Q1; S = sine is + in Q2; T =
tangent is + in Q3; C = cosine is + in Q4.
Inverse
trig functions:
y = sin-1 x:
answers will be in Q1 or Q4, use symmetry to get other answers.
y = cos-1 x:
answers will be in Q1 or Q2, use symmetry to get other answers.
y = tan-1 x:
answers will be in Q1 or Q4, use symmetry to get other answers.
Know
the domains and ranges of the inverse trig functions.
Know midline, amplitude,
period based on graphs!!!
Basic
Identities:
sin2
x + cos2 x = 1
(Corollaries: sin2 x
= 1 - cos2 x, cos2
x = 1 - sin2 x)
sin
(2x) = 2 sin x cos x
cos
(2x) = cos2 x - sin2 x = 2cos2
x - 1 = 1 - 2sin2 x.
(shift identities)
sin(-x)
= -sin(x), tan(-x) =
-tan(x) (sine and tangent are
odd functions)
cos(-x)
= cos(x) (cosine is an
even function)
Right
Triangles:
"Soh-Cah-Toa". Remember, csc x = 1/sin x, sec x = 1/cos x, cot x = 1/tan x.
Use
Pythagoras' formula to determine unknown sides in a right triangle.
Law
of Cosines: (Used in SAS or SSS triangles)
Lower
case a, b, c are always sides, Capital A, B,
C are angles. A is
opposite a, etc.
. Analogous
formulas for a and b.
Law
of Sines:
Make
sure you're in the right mode (degree/radian).