Download Finding Reference Angles and Trigonometric Values and more Exams Analytical Geometry and Calculus in PDF only on Docsity!
Reference Angles
REFERENCE ANGLE : a positive acute angle made by the terminal side of
an angle and the x axis. Quadrant I Quadrant IIQuadrant IIIQuadrant IV reference^. reference = 180 o^ θ Find the reference angle for each given angle. EX 1 210 o^ EX 2 300 o^ EX 3 240 o^ EX 4 1035 o Quadrant III 210 o^180 o^ = 30 o reference = 30 o Quadrant IV 360 o^300 o^ = 60 o reference = 60 o^ reference = 60 o Quadrant II 180 o^120 o^ = 60 o 240 o^ + 360 o^ = 120 o coterminal angle reference = 45 o Quadrant IV 360 o^315 o^ = 45 o 1035 o^ 2(360 o) = 315 o coterminal angle reference = (^) θ 180 o^ reference = 360 o^ θ
Quadrant II Quadrant I Quadrant III Quadrant IV reference = 180 o^ θ reference reference = 360 o^ θ θ Reference Angle 30 o^30 o 45 o^45 o 60 o^60 o θ Reference Angle 120 o^60 o 135 o^45 o 150 o^30 o reference = (^) θ 180 o θ Reference Angle 210 o^30 o 225 o^45 o 240 o^60 o θ Reference Angle 300 o^60 o 315 o^45 o 330 o^30 o
If the degree ends in a 5 , then it has a reference angle of 45
o .
If the degree's middle number is ODD, then it has a reference angle of 30
o .
If the degree's middle number is EVEN, then it has a reference angle of 60
o .
All Students Take Classes 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, 45 o, 60 o). Step 4: Determine the value for the given reference angle. Finding the Trigonometric Values of Special Angles EX 8 csc 60 o^ EX 9 sec 210 o^ EX 10 cot 135 o
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, 360 o]. EX 11 EX 12 EX 13 EX 14
