section 1.1: radian degree measure. objective: to be able to sketch an angle in radians and find...

TRIGONOMETRY

Section 1.1: Radian & Degree Measure

Objective: To be able to sketch an angle in radians and find the quadrant of the terminal side.

Trigonometry is the branch of mathematics dealing with the relations of the sides and angles of triangles and with the relevant functions of any angles.

An angle is the space between two lines, segments or rays with a common endpoint. Created by rotating a ray about its endpoint.

Standard position: Naming angles:

Positive angles rotate in a counter clockwise direction.Negative angles rotate in a clockwise direction.

Radian Measure: One radian is the measure of the central angle, , that intercepts an arc, s, equal in length to the radius of the circle, r.

Therefore .

A central angle is any angle whose vertex is the center of the circle.

Circumference of a circle:

Common Angle Measurements:

Quadrants:

Revolutions Radians Degrees

1

½

¼

Examples: Sketch the angle and determine the quadrant of the terminal side of each angle.a. b.

c. d. 5

e. 3.77 f. -

Try these:g. h.

End day 1

Coterminal Angles: angles with the same initial side and same terminal side are called coterminal angles.

Ex.) Let . Draw a sketch of the angle, , and one that is coterminal to .

» A given angle has an infinite number of coterminal angles.» The coterminal angle for any angle can be found by adding or

subtracting where n is any integer.or

Example: Find one positive and one negative angle that is coterminal to .a. b.

c. d.

e. 4.13 f.

Complementary and Supplementary AnglesTwo positive angles, and , and complementary if their sum is . (or )

Two positive angles, and , and supplementary if their sum is . (or )

Example: If possible, find the complement and the supplement of a. b.

c. d.

e. f.

Converting from Degrees to Radians:

Example: Convert the following angles from degrees to radians:a. b. c.

Converting from Radians to Degrees:

Example: Convert the following angles from radians to degrees:a. b. c.

Review Question:Given a. Sketch the angle and determine the quadrant that the

terminal side falls.

b. Find one positive and one negative coterminal angle of .

c. If possible, find the complement and supplement of .

d. Convert to degrees.