Trigonometry Review with the Unit Circle: All the trig. you’ll ever need to know in Calculus
Objectives: This is your review of trigonometry: angles, six trig. functions, identities and formulas, graphs: domain, range and transformations.

Angle Measure Angles can be measured in 2 ways, in degrees or in radians. The following picture shows the relationship between the two measurements for the most frequently used angles. Notice, degrees will always have the degree symbol above their measure, as in “452 ° ”, whereas radians are real number without any dimensions, so the number “5” without any symbol represents an angle of 5 radians. An angle is made up of an initial side (positioned on the positive x-axis) and a terminal side (where the angle lands). It is useful to note the quadrant where the terminal side falls. Rotation direction Positive angles start on the positive x-axis and rotate counterclockwise. Negative angles start on the positive x-axis, also, and rotate clockwise. Conversion between radians and degrees when radians are given in terms of “ π ” DEGREES RADIANS: The official formula is θ ⋅

π
180

= θ radians

Ex. Convert 120 into radians

SOLUTION: 120 ⋅

π
180

=

2π radians 3

RADIANS

DEGREES: The conversion formula is θ radians ⋅

180

π

=θ

Ex. Convert

π
5

into degrees.

SOLUTION:

π 180 180 ⋅ = = 36 5 π 5

For your own reference, 1 radian ≈ 57.30

A radian is defined by the radius of a circle. If you measure off the radius of the circle, then take the straight radius and curved it along the edge of the circle, the angle this arc marks off measures 1 radian.

Arc length: when using radians you can determine the arc length of the intercepted arc using this formula: Arc length = (radius) (degree measure in radians) OR s = rθ There may be times you’ll use variations of this formula.

Ex. Find the length