Trig Functions of right triangles

Notes:

Remember SOHCAHTOA? - Sine with Opposite length OVER the Hypotenuse

  • Cosine with Adjacent length OVER the Hypotenuse

and finally,

  • Tangent with Opposite length OVER the Adjacent length

Don’t forget their inverses as well…

  • Cosecant with Hypotenuse OVER the Opposite length

  • Secant with Hypotenuse OVER the Adjacent length

and finally,

  • Cotangent with Adjacent length OVER the Opposite length

Well… the Pythagorean Theorem applies! The acute angles are complementary & add up to 90˚.

This (these?) definition(s) is a subset of our previous definitions.

Formulas / Terms

Fundamental Identities:

  • tan(ø) = sin(ø) / cos(ø)

  • tan(ø) = 1 / cot(ø)

  • cot(ø) = cos(ø) / sin(ø)

  • sec(ø) = 1 / cos(ø)

  • csc(ø) = 1 / sin(ø)

Co-function Identities:

  • Degrees:

    • cos(ø) = sin(90˚ - ø)
    • cot(ø) = tan(90˚ - ø)
    • csc(ø) = sec(90˚ - ø)

  • Radians:

    • cos(ø) = sin((π / 2) - ø)

    • cot(ø) = tan((π / 2) - ø)

    • csc(ø) = sec((π / 2) - ø)

Pythagorean Identities:

  • sin2(ø) + cos2(ø) = 1

  • 1 + tan2(ø) = sec2(ø)

  • cot2(ø) + 1 = csc2(ø)

  1. (Opposite / Hypotenuse)2 + (Adjacent / Hypotenuse)2 ?= 1

  2. (Opposite2 + Adjacent2) / Hypotenuse2 ?= 1

  3. Hypotenuse2 / Hypotenuse22 = 1