Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
12.2 DAY 1: FUNCTIONS OF ANY ANGLE VOCABULARY An angle is formed by two rays that have a common endpoint, called the vertex. ANGLE INITIAL SIDE TERMINAL SIDE STANDARD POSITION The fixed ray of an angle. The ray that rotates about the vertex to get the desired angle. In a coordinate plane, an angle whose vertex is at the origin and whose initial side is the positive x-axis is in standard position. The angle measure is POSITIVE if the rotation of an angle’s terminal side is COUNTERCLOCKWISE. The angle measure is NEGATIVE if the rotation of an angle’s terminal side is CLOCKWISE. ANGLE MEASURE POSITIVE VS. NEGATIVE REFERENCE ANGLE Find reference angles: Sketch each angle. Then find its reference angle. 300 115 135 150 Angles are coterminal if their terminal sides coincide. An angle coterminal with a given angle can be found by adding or subtracting multiples of ______. Example: COTERMINAL Find one positive angle and one negative angle that are coterminal with a 95 degree angle. 95________________ = __________ 95 ________________ = __________ 12.2 DAY 2: FUNCTIONS OF ANY ANGLE RADIANS AND DEGREES Angles can be measured in degrees or radians just like distance can be measured in many different ways. Radians are units that are based on arc length and circumference. RADIANS CONVERT BETWEEN DEGREES AND RADIANS 180 radians Degrees to Radians Radians to Degrees To convert from degrees to radians, multiply the number of degrees by To convert from radians to degrees, multiply the number of radians by Degrees radians 1 180 radians 180 radians Rewrite each degree measure in radians and each radian measure in degrees. 1. 330 5 2. 3. 6 3 4. 50 5. 190 Remember the two special right triangle patterns: 6. 7 3 12.2 FUNCTIONS OF ANY ANGLE FINDING EXACT VALUES SIGNS OF TRIGONOMETRIC FUNCTIONS S A T C A S T C Draw the given angle and then determine whether the sine, cosine, and tangent functions of the given angle are positive or negative. 1. 80 2. 115 Sin 80 Cos 80 Tan 80 3. 325 Sin 115 Cos 115 Tan 115 Sin 325 Cos 325 Tan 325 4. 160 Sin 160 Cos 160 Tan 160 12.1 Day 3: NOW WE HAVE TO PUT EVERYTHING TOGETHER! Use a reference angle to find an Exact Trigonometric Value: 1. 2. 3. 4. 5. Draw in the terminal side of the angle. Determine the reference angle. Draw in your special right triangle. Use SOH CAH TOA to find the value. Use A S T C to determine if the value is positive or negative. sin 210 Reference Angle: ___________ SOH CAH Positive or TOA Negative sin 210 _________ 5. cos 150 6. tan 315 Reference Angle: ___________ Positive or Negative Reference Angle: ___________ cos 150 _______ Positive or Negative tan 315 _______ 8. cot 210 7. csc 225 Reference Angle: ___________ Reference Angle: ___________ Positive 9. cos or Negative csc 225 _______ 5 3 10. sec Reference Angle: ___________ Positive Positive or Negative or Negative cot 210 _______ 11 6 Reference Angle: ___________ cos 5 _______ 3 Positive or Negative sec 11 ________ 6 12.2 DAY 4: FUNCTIONS OF ANY ANGLE FINDING EXACT VALUES Evaluate Trigonometric Functions Given a Point: Find the sin, cos, and tangent 1. 2. QUADRANTAL ANGLES Evaluate the following. 3. 4. Sin 270 = ______ Csc 270 = ______ Sin -90 = ______ Csc -90 = ______ Cos 270 = ______ Sec 270 = ______ Cos -90 = ______ Sec -90 = ______ Tan 270 = ______ Cot 270 = ______ Tan -90 = ______ Cot -90 = ______