Chapter 4: Trigonometric Functions

Degrees ---> DMS

99.37°: .37 x 60 = 22', .2 x 60 = 12". 99°22'12"

Central Angle

A central angle is an angle whose apex (vertex) is the center θ of a circle and whose legs (sides) are radii intersecting the circle in two distinct points A and C. The central angle is subtended by an arc between those two points, and the arc length is the central angle times the radius.

Radians ---> Degrees

R*(180°/π)

Period

2π/B (π/B for tan/cot)

DMS ---> Degrees

48°30'36": 36/60 = .6, 30.6/60 = .51 48.51

Angular Velocity Formula

w = θ/t w = angular velocity, θ = angle measure (radians), t = time

Domain of tan and sec

{x|x∈ R≠((π/2)+kπ)}

Domain of csc and cot

{x|x∈ R≠kπ}

Amplitude

A value (sin and cos only)

Supplementary

Adds to 180°

Complementary

Adds to 90°

All Students Take Calculus

All positive in Quadrant I, sin positive in Quadrant II, tan positive in Quadrant III, cos positive in Quadrant IV

Domain of sin and cos

All reals

Standard Position (Terminal and Initial Side)

An angle is in standard position if its vertex is located at the origin and one ray is on the positive x-axis. The ray on the x-axis is called the initial side and the other ray is called the terminal side.

Transforming Trig Graphs

Asin(B(x+C))+D BCAD

Coterminal Angle

Coterminal angles are angles in standard position (angles with the initial side on the positive x-axis) that have a common terminal side. For example 30°, -330° and 390° are all coterminal.

Degrees ---> Radians

D°*(π/180°)

REMEMBER!

Label all answers and AXES!!!

SOHCAHTOA

Sine: Opposite, Hypotenuse (Cosecant opposite) Cosine: Adjacent, Hypotenuse (Secant opposite) Tangent: Opposite, Adjacent (Cotangent opposite)

Reference Angle

The reference angle is always the smallest angle that you can make from the terminal side of an angle (where the angle ends) with the x-axis. (Must be positive and acute)

Linear Velocity Formula

V = s/t OR V = rw V = linear velocity, s = distance covered (arc length), t = time V = linear velocity, r = radius, w = angular velocity

Arc Length Formula

s = rθ s = arc length, r = radius, θ = angle in radians