trigonometric identities
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Trigonometric functions
Sine Cosecant
Cosine Secant
Tangent Cotangent
Eight Fundamental
Trigonometric
Identities
Trigonometric Identity
- an equation that involves trigonometric functions which is true to any solution.
Reciprocal Relation
sin Ѳ = 1/cscѲ
cosѲ = 1/secѲ
tanѲ = 1/cotѲ
Quotient Relation
tanѲ = sinѲ/cosѲcotѲ = cosѲ/sinѲ
Pythagorean Relation
sin2Ѳ + cos2Ѳ = 1
1 + cot2Ѳ = csc2Ѳ
tan2Ѳ + 1 = sec2Ѳ
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.
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.)
1.cotѲ sinѲ = cosѲ
Ѳ- cscѲ = Ѳ- sinѲ)/
ᶿ = (1+sinᶿ)(1-sinᶿ)
cscᶿ tanᶿ = secᶿ
secᶿ = + cosᶿ
EvaluationProve the following:
1. secᶿ cotᶿ = cscᶿ 4. ᶿ - 1 =
2. + = 1 5. secᶿ + cscᶿ = cscᶿ (tanᶿ + 1)
3. ᶿ - 1 =
Assignment
Prove the following:
1. secѲ/cscѲ = tanѲ
2. cosѲtanѲ = sin Ѳ
3. cotѲsinѲ = cosѲ
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