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