Tips For LearningTrig Rules

Reciprocal Rules

Learn:

xx sec1cos xx cos

1sec

xx csc1sin x

xsin1csc

xx cot1tan

xx tan1cot

xxx cos

sintan xxx

sincoscot

Pythagorean Identities

xx

x

x

x2cos

12cos

2sin2cos

2cos

1. Learn

2. Derive the others by dividing.

12sin2cos xx

is xx 2sec2tan1

xx

x

x

x2sin

12sin

2sin2sin

2cos is xx 2csc12cot

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.