Survey
* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project
Download Reference Angles
Document related concepts
no text concepts found
Transcript
Reference Angles REFERENCE ANGLE : a positive acute angle made by the terminal side of an angle and the xaxis. Quadrant I Quadrant IIQuadrant IIIQuadrant IV . reference reference = 180o θ reference = θ 180o reference = 360o θ Find the reference angle for each given angle. EX 1 210o EX 2 300o EX 3 240 o EX 4 1035o 240o + 360o = 120o 1035o 2(360o) = 315o coterminal angle Quadrant III 210o 180o = 30o reference = 30o Quadrant IV 360o 300o = 60o reference = 60o Quadrant II 180o 120o = 60o reference = 60o coterminal angle Quadrant IV 360o 315o = 45o reference = 45o Quadrant I Quadrant II reference = 180o θ reference θ Reference Angle θ Reference Angle 120 o 60 o 30o 30 o 135 o 45 o 45o 45 o 150 o 30 o 60o 60 o Quadrant IV Quadrant III reference = θ 180o reference = 360o θ θ Reference Angle θ Reference Angle 210 o 30 o 300 o 60 o 225 o 45 o 315 o 45 o 240 o 60 o 330 o 30 o 5, then it has a reference angle of 45o. If the degree ends in a 30o. o If the degree's middle number is EVEN, then it has a reference angle of 60 . If the degree's middle number is ODD, then it has a reference angle of Finding the Trigonometric Values of Special Angles Step 1: Determine what quadrant the angle is in. Step 2: Determine whether or not the value will be positive or negative. Step 3: Find the reference angle (30o, 45o, 60o). Step 4: Determine the value for the given reference angle. All Students Take Classes EX 5 sin120o EX 6 cos225o EX 7 tan 330o Finding the Trigonometric Values of Special Angles Step 1: Determine what quadrant the angle is in. Step 2: Determine whether or not the value will be positive or negative. Step 3: Find the reference angle (30o, 45o, 60o). Step 4: Determine the value for the given reference angle. All Students Take Classes EX 8 csc 60o EX 9 sec 210o EX 10 cot 135o Finding Angle Measures Given Trigonometric Function Values Step 1: Find the quadrants of the trigonometric function by its charge. Step 2: Find the reference angle by the function value. Step 3: Use the reference angle to find its angle measure, , in the interval of [0o, 360o]. EX 11 EX 12 EX 13 EX 14
Related documents