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Trigonometric Functions of Any Angle

Trigonometric Functions of Any Angle. Pre-Calculus Unit #4: Day 3. Coterminal Angles. Coterminal angles are angles in standard position (angles with the initial side on the positive x -axis) that have a common terminal side.  For example 30°, –330° and 390° are all coterminal .

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Trigonometric Functions of Any Angle

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  1. Trigonometric Functions of Any Angle Pre-Calculus Unit #4: Day 3

  2. Coterminal Angles • Coterminal angles are angles in standard position (angles with the initial side on the positive x-axis) that have a common terminal side.  • For example 30°, –330° and 390° are all coterminal. http://hotmath.com/hotmath_help/topics/coterminal-angles.html

  3. Example: • Find a positive and a negative angle coterminal with a 55° angle. • 55° – 360° = –305° • 55° + 360° = 415° http://hotmath.com/hotmath_help/topics/coterminal-angles.html

  4. Complementary Angles • Complementary angles are two angles whose measures add up to 90o. http://hotmath.com/hotmath_help/topics/complementary-angles.html

  5. Example: • 1 = 2x+1 and  2 =3x+4. If these angles are complements, then what is the value of x?

  6. Supplementary Angles • Supplementary angles are two angles whose measures add up to 180o. http://hotmath.com/hotmath_help/topics/supplementary-angles.html

  7. Example: Find the supplement of each of the following given angles: a.) 65° b.) 109° c.) 4z°

  8. Quadrants S A C T

  9. Finding Trig Ratios for Any Angle • Determine the quadrant of the given angle. • Draw a right triangle to find the missing side of the triangle. (Pythagorean Thm.) • Set up the trig functions using the appropriate signs.

  10. Example: • Given that and  is in the second quadrant, find the other 5 function values.

  11. Reference Angles and Exact Values • The reference angle is the acute angle formed by the terminal side of the given angle and the x-axis. 

  12. Examples:

  13. Homework • Page 511-512, • #2-24 even, 34-52 even

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