Tips For Learning Trig Rules

Reciprocal Rules Learn:

Pythagorean Identities 1.Learn 2.Derive the others by dividing. is

Co-Function Rules Remember that cofunction rules come from complementary angles (meaning they sum to 90 o 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 cos 2 x, sin 2 x, tan 2 x 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 90 o – x in the angle, use cofunction rules.