presentation of trigonometry identities
Answers
Answer:
1. Trigonometric functions Sine Cosecant Cosine Secant Tangent Cotangent
2. Eight Fundamental Trigonometric Identities
3. Trigonometric Identity - an equation that involves trigonometric functions which is true to any solution.
4. Reciprocal Relation sinѲ = 1/cscѲ cosѲ = 1/secѲ tanѲ = 1/cotѲ
5. Quotient Relation tanѲ = sinѲ/cosѲ cotѲ = cosѲ/sinѲ
6. Pythagorean Relation sin2Ѳ + cos2Ѳ = 1 1 + cot2Ѳ = csc2Ѳ tan2Ѳ + 1 = sec2Ѳ
7. CONDITIONS: 1.Transposition is not allowed. 2.Transform expressions independently. 3. Do not divide or multiply a common term to both sides of the equation. 4.Transform the complicated side.
8. useful rules: 1. Memorize the 8 trigonometric identities. 2. Express all functions in terms of sine and cosine. 3. Be familiar with algebra, manipulations (factoring, special products, combining like terms, simplifying complex fraction.)
9. 1.cotѲ sinѲ = cosѲ 2. 2 Ѳ- cscѲ = (2 Ѳ- sinѲ)/ 2Ѳ
10. 2 ᶿ = (1+sinᶿ)(1-sinᶿ) cscᶿ tanᶿ = secᶿ secᶿ = 2 ᶿ ᶿ + cosᶿ
11. Evaluation Prove the following: 1. secᶿ cotᶿ = cscᶿ 4. 22ᶿ - 1 = 2ᶿ−2ᶿ ᶿᶿ 2ᶿ+2ᶿ ᶿᶿ 2. ᶿ ᶿ + ᶿ ᶿ = 1 5. secᶿ + cscᶿ = cscᶿ (tanᶿ + 1) 3. 22 ᶿ - 1 = ᶿ−ᶿ ᶿ+ᶿ
12. Assignment Prove the following: 1. secѲ/cscѲ = tanѲ 2. cosѲtanѲ = sin Ѳ 3. cotѲsinѲ = cosѲ
Answer:
Using Formula 2cos²ѳ-1=cos2ѳ, prove that