Download 4.1

Chp 4.1
Radian and Degree Measure (pg. 282)
CA Standard:
Trigonometry
1.0
Objective:
To measure
angle and
convert
between
degrees to
radians.
Angle
Bellwork
1. Condense.
⅓[ln(x + 1) + 3ln(x – 1)] + ½lnx
2. Solve for x.
a. log x + log(x + 9) = 1
b. 33x+1 = 5
An angle is determined by rotating a ray about its endpoint.
Angle in An angle in standard position has the vertex at the origin and the initial
Standard side coincides with positive x-axis.
Position
Coterminal Coterminal angles are angles with the same initial and terminal sides.
Angles
Example 1 Sketch the measure and find the coterminal angle.
a. 390°
b. 135°
c. –120°
Complementary The sum of two positive angles are complementary if their sum is π/2.
and
Supplementary The sum of two positive angles are supplementary if their sum is π.
Angles
Example 2 If possible, find the complementary and
supplementary angles.
a. 72°
b. 148°
Radian One radian is the measure of a central angle θ that intercepts an arc s
Measure equal to the radius r of a circle. (θ = r/s radians or arc length is s = rθ)
Arc length s is the circumference of a unit circle (r = 1). Therefore, one
revolution is s = 2π. So, 360° = 2π.
Common The angles below are the most used in this course.
Angles
Example 3 Find each angle.
a. The complement of θ =
b. The supplement of θ =

12
5
6
.
c. The coterminal angle of θ =
.
17
6
.
Conversions To convert degrees to radians, multiply by
π radians/180°.
To convert radians to degrees, multiply by 180°/π radians.
Example 4 Convert.
a. 135°
b. 540°
c.


d. 2 radians
2
DMS To DD Use your calculator to go from Degree Minute Second (DMS) to Degree
Decimals (DD). 23 15' 21" =