TRIGONOMETRY. Trigonometry Comes from two Greek words trigonon and metron, meaning “triangle measurement”. 7.1 Measurement of Angles. DEGREES-unit of measure for angles 360 °=1 revolution Revolution –one complete circular motion Minutes- 1°=60 minutes (60’)
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Comes from two Greek words trigonon and metron, meaning“triangle measurement”
Revolution –one complete circular motion
Minutes- 1°=60 minutes (60’)
Seconds-1’ =60 seconds(60”)
The measure of the central angle that intercepts
the arc is
= s/r radians.
RADIAN-unit of measure for angles 2π=1 revolution
Converting radians to degrees
An angle is formed by two rays that have a common endpoint called the vertex. One ray is called the initial side and the other the terminalside. The arrow near the vertex shows the direction and the amount of rotation from the initial side to the terminal side.
Positive angles rotate counterclockwise.
Negative angles rotate clockwise.
xº+ k· 360º
where k is an integer.Coterminal Angles
Assume the following angles are in standard position. Find a positive angle less than 360º that is coterminal with:
a. a 420º angle b. a –120º angle.
Solution We obtain the coterminal angle by adding or subtracting 360º. Our need to obtain a positive angle less than 360º determines whether we should add or subtract.
a. For a 420º angle, subtract 360º to find a positive coterminal angle.
420º – 360º = 60º
A 60º angle is coterminal with a 420º angle. These angles, shown on the next slide, have the same initial and terminal sides.
±2πExamples- find two angles, one positive and one negative, that are coterminal with each given angle