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Lesson _______ Section 4
Lesson _______ Section Intro to Trigonometry: Radian & Degree Measure Triangle Measurements Vocabulary Origin & Quadrants Vertex Right, Acute, & Obtuse Complementary & Supplementary Central & Inscribed Angles Arc
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An ANGLE is created by rotating a ray about its endpoint (vertex).
Terminal Side Initial Side If we fit an angle to a coordinate system, the vertex is at the _______ and the initial side is the _________ This is called “Standard Position”
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Positive Angle (Counterclockwise)
Negative Angle (Clockwise) These 2 angles are “COTERMINAL” (They end together) Ex. Find 2 angles that are coterminal with 100°
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Angles can be measured in DEGREES or in RADIANS (similar to feet & meters)
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s r If s = r then = 1 radian
DEF: One RADIAN is the measure of a central angle such that the arc length s is equal to the length of the radius r. s If s = r then = 1 radian r
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The radian measure of a central angle
10 5 1 rad. 2 rad. 5 5 The radian measure of a central angle = arc length s r = radius
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= s r 360° 180° 90° 60° 45° 30° ? ½ a revolution? ¼ a revolution? 2
Radians Degrees 360° 1 full revolution? ½ a revolution? 180° ¼ a revolution? 90° 60° s r = 45° 30° ? 2
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Sketch the following angles:
Ex.
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Ex. What is the supplement of ?
Ex. What is the complement of ? Ex. Find 2 coterminal angles for for
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THETA must be measured in RADIANS!
ARC LENGTH FORMULA s r = s r = THETA must be measured in RADIANS!
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