Trig Unit circle and Inverse Functions

What is the domain and range of arctan?

Domain: [ -∞, ∞ ] Range: [ -π/2. π/2 ]

Π/3 is how many degrees and what are the values of sin and cos at this angle?

60 cos = 1/2 sin = √3/2

Π/2 is equal to how many degrees and what are the values of cos and sin at this angle?

90 cos = 0 sin = 1

What is a unit circle?

A circle centered at the point (0,0) with a radius of 1. Sin and Cos correspond to y and x respectively.

What is the range (output) of tan and cot?

All real numbers

What is the domain (input) of csc and cot?

All real numbers except 0 (+ k * 2π) AND π (+k *2π) Basically any revolution where sin θ = 0 they are undefined

What is the domain (input) of tan and sec?

All real numbers except: π/2 (+ k * 2π) AND 3π/2 (+ k *2π) Basically any revolution where cos θ = 0 they are undefined.

The Domain (input) of sin and cosine is _____

All real numbers.

What are coterminal angles?

Angles with the same terminal side. Just add/subtract 360° (or 2π) to find them.

What is the range (output) for csc and sec?

Any number except those between -1 and 1. The opposite of sin and cos

What is the domain and range of arcsin?

Domain: [ -1, 1 ] Range: [ -π/2 , π/2 ]

What is the domain and range of arccos?

Domain: [ -1, 1 ] Range: [ 0, π ]

Instead of (trig function)⁻¹ another name for each inverse is?

arcsin, arccos, arctan etc

If the angle given in a unit circle is positive it rotates _____ and if it is negative it rotates _____

counterclockwise, clockwise

Pattern(s) for memorizing the unit circle DEGREES?

1) The 4 main quadrant lines go 0°, 90°, 180°, 270°, 360° 2) In between the 90° increments the degrees increase in a pattern of: 30°, 45°, 60°

For memorizing the unit circle in RADIANS, what is the pattern for the NUMERATORS in each quadrant?

2) Numerator of quad 1 is just π 3) Numerator of quad 2 is (denominator -1) * π 4) Numerator of quad 3 is (denominator +1) * π 5) Numerator of quad 4 is ((2*denominator)-1) *π

What does a circle measure in radians?

2Π which is equal to 360 degrees which in turn is 1 revolution.

Π/6 is equal to how many degrees and what are the values of sin and cos at this angle?

30 cos = √3/2 sin = 1/2

Π/4 is equal to how many degrees and what are the values of sin and cos at this angle?

45 cos = √2/2 sin = √2/2

What is a radian?

It is ≈ 57.3°

Periodic Properties of tan, sec, csc and cot?

Revolving all the way around the circle gets the same trig ratio for Sec and Csc. Revolving in halfway increments gets the same trig ratio for Tan and Cot. Sec and Csc have period 2π (360°). Tan and Cot have period π (180°).

Periodic Properties of sin and cos?

Revolving all the way around the circle gets you the same trig ratio. Sin and Cos have period 2π (360°)

For memorizing the unit circle in RADIANS what is the pattern for the DENOMINATORS in each quadrant?

The denominator decreases by 6, 4, 3 from the x-axis to y-axis.

What is the range (output) for sin and cos?

[ -1, 1 ]

Inverse Trigonometric Functions always return a ____

angle