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TRIGONOMETRY

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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TRIGONOMETRY

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  1. TRIGONOMETRY Trigonometry Comes from two Greek words trigonon and metron, meaning“triangle measurement”

  2. 7.1 Measurement ofAngles

  3. DEGREES-unit of measure for angles 360°=1 revolution Revolution –one complete circular motion Minutes- 1°=60 minutes (60’) Seconds-1’ =60 seconds(60”) 1°=3600”

  4. Convert to degrees only

  5. Convert to degrees only

  6. Convert to DMS

  7. Convert to DMS

  8. Consider an arc of length s on a circle of radius r. The measure of the central angle that intercepts the arc is  = s/r radians. s  r O r Radian Measure

  9. Definition of a Radian • One radian is the measure of the central angle of a circle that intercepts an arc equal in length to the radius of the circle. RADIAN-unit of measure for angles 2π=1 revolution

  10. Converting degrees to radians Converting radians to degrees

  11. Example 240° Example -315°

  12. Example Example

  13. C A Initial Side Terminal Side θ Vertex B Angles 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.

  14. y y is positive Terminal Side  Vertex Initial Side x x Vertex  Terminal Side Initial Side is negative Positive angles rotate counterclockwise. Negative angles rotate clockwise. Angles of the Rectangular Coordinate System • An angle is in standard position if • its vertex is at the origin of a rectangular coordinate system and • its initial side lies along the positive x-axis.

  15. An angle of xº is coterminal (have the same terminal ray) with angles of xº+ k· 360º where k is an integer. Coterminal Angles

  16. Example 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.

  17. y y 240º 60º x x 420º -120º Example cont. Solution b. For a –120º angle, add 360º to find a positive coterminal angle. -120º + 360º = 240º A 240º angle is coterminal with a –120º angle. These angles have the same initial and terminal sides.

  18. 10° 100° -5° 400° π π/2 -π/3 4π 370°,-350° 460°,-260° 355°,-365° 40°,-320° 3π,-π 5π/2,-3π/2 5π/3,-7π/3 ±2π Examples- find two angles, one positive and one negative, that are coterminal with each given angle

  19. ASSIGNMENT • Page 261 #1-10, 12-32 (even)

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