Identities

Notes:

“Semantic memory” = facts

“Episodic memory” = stories, visualization

“Complimentary Sine” = Cosine

All of our Identities still work!

Standard 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)

Cofunction Identities:

  • 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)

Our last way of defining the trig functions (last one, I promise):

Let ‘t’ be an angle in standard position.

Let (x, y) be any point on the terminal side of ‘t’.

Let ‘r’ be the distance from (x, y) to the origin. Which basically means… ‘r’ cannot be more than one because the max radius on the unit circle is 1.

  • sin(t) = (y / r)

  • cos(t) = (x / r)

  • tan(t) = (y / x)

  • sec: (r / x)

  • csc: (r / y)

  • cot: (x / y)

Formulas / Terms

Formula for the area of a triangle that has side lengths a and b and the angle between a and b measuring ø:

  • A = (1 / 2) • a • b • sin(ø)

The Reference Angle:

The Reference Angle of an angle ‘t’ in standard position, tref, is the acute angle formed by the terminal side of ‘t’ and the x-axis.