GEOMRTRY: Trigonometric Identities Formula (Laws & Identities)

sin²θ + cos²θ = 1

tan²θ + 1 = sec²θ
cot²θ + 1= csc²θ

What are the Three (3) PYTHAGOREAN IDENTITES

1

What is the value of sin²θ + cos²θ ?

sec²θ

What is the value of tan²θ + 1 ?

csc²θ

What is the value of cot²θ + 1 ?

sin(a + b) = sin(a)cos(b) + cos(a)sin(b)
cos(a + b) = cos(a)cos(b) - sin(a)sin(b)
tan(a + b) = [tan(a) + tan(b)] / [1 - tan(a)tan(b)]

What are the SUM & DIFFERENCE IDENTITIES

sin(a)cos(b) + cos(a)sin(b)

sin(a + b) ?

cos(a)cos(b) - sin(a)sin(b)

cos(a + b)

[tan(a) + tan(b)] / [1 - tan(a)tan(b)]

tan(a + b)

sin(2x) = 2sin(x)cos(x)

cos(2x)

= cos²(x) - sin²(x)

= 1 - 2sin²(x)

= 2cos²(x) - 1

tan(2x) = [2tan(x)] / [1 - tan²(x)]

What are the double angle formulas ?

2sin(x)cos(x)

sin(2x) ?

= cos²(x) - sin²(x)

= 1 - 2sin²(x)

= 2cos²(x) - 1

cos(2x) ?

[2tan(x)] / [1 - tan²(x)]

tan(2x) ?

sin(x/2) = plus minus sqrt{[1 - cos(x)] / 2}
cos(x/2) = plus minus sqrt{[1 + cos(x)] / 2}
tan(x/2) = plus minus sqrt{[1 - cos(x)] / [1 + cos(x)]}

What are the half angle formulas ?

plus minus sqrt{[1 - cos(x)] / 2}

sin(x/2) ?

plus minus sqrt{[1 + cos(x)] / 2}

cos(x/2) ?

plus minus sqrt{[1 - cos(x)] / [1 + cos(x)]}

tan(x/2) ?

sinA/a = sinB/b = sinC/c (vise versa)

State the LAW OF SINES

a² = b² + c² - 2bc(cosA)

b² = a² + c² - 2ac(cosB)

c² = a² + b² - 2ab(cosC)

State the LAW OF COSINES