Parity and reduction formulas
Find out that sine, tangent and cotangent are odd and cosine is even, then use the reduction rule: when the function changes its name and which sign it gets.
- France: grade 11
- Germany: grade 10
- Ukraine: grade 10
- Russia: grade 10
Guide
For Ukrainian Grade 10 (algebra and analysis, section 2, items 10 and 14). Angles are in radians; tangent and cotangent are written tg and ctg in Ukraine.
For every α: sin (−α) = −sinα, tg (−α) = −tgα, ctg (−α) = −ctgα and cos (−α) = cosα. So cosine is even and the others are odd.
Reduction formulas for π2±α, π±α, 3π2±α and 2π − α follow a rule. Step 1: with π or 2π the function keeps its name; with π2 or 3π2 it changes to its co-function (sin to cos, tg to ctg and back). Step 2: put the sign that the left side has, treating α as an acute angle.
Common slips: forgetting the name change for π2 and 3π2; taking the sign of the result instead of the left side; thinking sine is even.