Download Precalculus Name Student Notes 4.1 – 4.4 4.1 Radian and Degree

Precalculus
Student Notes 4.1 – 4.4
Name __________________________________________
4.1 Radian and Degree Measure
COTERMINAL ANGLES:
Two angles that share the same initial and
terminal sides. (Different rotations, end up in the
same exact place.)
Angles in degrees that are coterminal will differ by 360⁰ (or multiples of 360⁰)
Angles in radians that are coterminal will differ by 2 (or multiples of 2 )
 

radians 
 or
2


COMPLEMENTARY ANGLES:
Two angles that add to 90⁰
SUPPLEMENTARY ANGLES:
Two angles that add to 180⁰ or 
Not all angles have a complement or supplement.
radians 
EXAMPLE: Convert the angles to radians. (Leave in terms of π)
EXAMPLE: Convert the angles to degrees.
DEGREES, MINUTES, SECONDS (DMS)
Another way to represent an angle measure
Instead of using the traditional decimal degrees (DD), some still use DMS.
(Think of a degree as an hour.) The “degree” concept remains the same, but the other conversions are:
60 minutes (60’) = 1⁰
60 seconds (60”) = 1 minute (1’)
Combining the two conversions, it takes 3600 seconds (3600”) to make 1⁰
EXAMPLE: Convert to decimal degrees (DD)
EXAMPLE: Convert to degrees, minutes and seconds (DMS)
 must be in radians
 must be in radians
EXAMPLES: Find the arc length and the area formed if
4.2 Trigonometric Functions: The Unit Circle
4.3 Right Triangle Trigonometry
4.4 Trigonometric Functions of Any Angle
Find the sine, cosine, tangent, cosecant, secant,
and cotangent for all the angles on your unit circle.
Properties of the Trigonometric Functions
Example 1: Use the fact that the trigonometric functions are periodic to find the exact value of
each expression. Do not use a calculator.
(d) sec 540º
(e) cot 420º
(f) csc 1215º
Determine the signs of the trigonometric functions in a given quadrant.
Example 2: Name the quadrant in which the angle θ lies.
(a)
(b)
Example 3: Sin θ and cos θ are given. Find the exact value of the four remaining trigonometric
functions.
(a)
(b)
Example 4: Find the exact value of each of the remaining trigonometric functions of θ.
(a)
(b)
(c)
(d)
Example 5: Use the even-odd properties to find the exact values of each expression. Do not use
a calculator.
Remember that I said EVERYTHING in trig boils down to sine and cosine.
If you can just figure out those two, you can figure out everything else.