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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
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