Tips For Learning
Trig Rules
Reciprocal Rules
Learn:
1
cos x  sec
x
1
sec x  cos
x
1
sin x  csc
x
csc x  1
sin x
tan x  1
cot x
cot x  1
tan x
sin x
tan x  cos
x
cot x  cos x
sin x
Pythagorean Identities
1. Learn
cos2 x  sin 2 x 1
2. Derive the others by dividing.
cos 2 x  sin 2 x  1
cos 2 x cos 2 x cos 2 x
cos 2 x  sin 2 x  1
sin 2 x sin 2 x sin 2 x
is
is
1 tan2 x  sec 2 x
cot2 x 1 csc 2 x
Co-Function Rules
Remember that cofunction rules come from complementary angles
(meaning they sum to 90o or π/2).
Therefore trig(x) = co-trig(π/2 – x). This works for any of the co---functions.
Example:
csc(x) = sec(π/2 – x)
Odd – Even Functions
Recall:
Even functions have f(-x) = f(x). (Symmetry about the y-axis)
Odd functions have f(-x) = -f(x) (Symmetry about the origin)
Remember:
cos and sec are the only even functions. All others are odd.
Therefore:
cos(-x) = cos(x) and sec(-x) = sec(x)
For all other functions follow the pattern:
sin(-x) = -sin(x) tan(-x) = -tan(x) etc
General Principles
1. If you see squares such as cos2x, sin2x, tan2x think
Pythagorean Identities.
2. If you have tan and cot mixed with sin and cos, use the
tan x = sin x / cos x rules.
3. If there are negatives in the angle such as sec(-x), use
odd/even rules.
4. If there are π/2 – x or 90o – x in the angle, use cofunction
rules.