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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.