Precalculus Trigonometry & Trigonometric Identities

Things Necessary For Test:

• A = ½ * a * b * sinθ

• SinA / a = SinB / b = SinC / b

• C = a² + b² - 2 * a * b * cosC

• Unit Circle Memorization

• Pythagoreon Identity

  • sin²x + cos²x = 1

  • cos²x = 1-sin²x

  • sin²x = 1-cos²x

  • tan²x+1 = sec²x

  • 1+cot²x = csc²x

• Odd/Even Identities

  • sin(-x) = -sin(x)

  • cos(-x) = cos(x)

  • tan(-x) = -tan(x)

• Fundamental Identities

  • cscx = 1/sinx

  • secx = 1/cosx

  • cotx = cosx/sinx

  • tanx = sinx/cosx

  • cotx = 1/tanx

• Understand the application of all stated above, show proficiency in both identities and formulas stated above and below:

  • These sum/difference identities:

    • sin(a±b) = sin(a)*cos(b) ± cos(a)*cos(b)

    • cos(a±b) = cos(a)*cos(b) -/+ sin(a)*sin(b)

    • tan(a±b) = (tan(a) ± tan(b)) / (1 -/+ tan(a)*tan(b))

  • These Double Angle Identities:

    • sin(2x) = 2sinx*cosx

    • cos(2x) = cos²x - sin²x

    • cos(2x) = 2cos²x - 1

    • cos(2x) = 1-2sin²x

    • tan(2x) = (2tanx)/(1-tan²x)

  • Half-Angle Identities:

    • sin(x/2) = ± √1-cos/2

    • cos(x/2) = ± √1+cosx/2

    • tan(x/2) = ± 1-cosx/sinx