Activity 4-2: Trig Ratios of Any Angles

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Presentation transcript:

Activity 4-2: Trig Ratios of Any Angles Part 2: Trigonometric Ratios and Reciprocal Trigonometric Ratios

Activity 4-2: Trig Ratios of Any Angles Part 2: Trigonometric Ratios and Reciprocal Trigonometric Ratios The reciprocal trigonometric ratios are the reciprocal of the primary ratios: Primary Ratio Reciprocal Ratio Sine Ratio sinθ = opposite/hypotenuse sinθ = y/r Cosecant Ratio cscθ =hypotenuse/opposite cscθ = r/y Cosine Ratio cosθ = adjacent/hypotenuse cosθ = x/r Secant Ratio secθ =hypotenuse/adjacent secθ = r/x Tangent Ratio tanθ = opposite/adjacent tanθ = y/x Cotangent Ratio cotθ =opposite/adjacent cotθ = x/y

Activity 4-2: Trig Ratios of Any Angles Part 2: Trigonometric Ratios and Reciprocal Trigonometric Ratios Let us try the following: Find the trigonometric and the reciprocal trigonometric ratios for θ = 7π/6 Step 1: Draw the angle on your unit circle. Since the denominator is 6, every π (180o) is broken into 6 parts. 3π/6 x y 4π/6 2π/6 QUADRANT 2 QUADRANT 1 5π/6 π/6 θ Step 2: Find your ratios. Remember that the angle is in the THIRD QUADRANT therefore, only TANGENT and COTENGENT are POSITIVE 6π/6 7π/6 7π/6 QUADRANT 3 TANGENT POSITIVE Step 2: Remember to change your calculator to radians. REMEMBER, your calculator may not give the proper sign. Use your drawn angle. QUADRANT 4 sin (7π/6) = -0.5 csc (7π/6) = 1/-0.5 = 2 cos (7π/6) = -0.866 sec (7π/6) = 1/-0.866 = -1.15 tan (7π/6) = 0.577 cot (7π/6) = 1.73

Activity 4-2: Trig Ratios of Any Angles Part 2: Trigonometric Ratios and Reciprocal Trigonometric Ratios Example 1) Find the trigonometric and reciprocal trigonometric ratio for the following angles. Try to solve before clicking to find the answer. a) 2 rads b) 3π/4 c) 11π/6 x y x y x y sin (2 rads) = 0.909 csc (2 rads) = 1.10 cos(2 rads) = -0.416 sec(2 rads) = -2.40 tan (2 rads) = -2.19 cot (2 rads) = -0.458 sin (3π/4 rads) = 0.707 csc (3π/4 rads) = 1.414 cos(3π/4 rads) = -0.707 sec(3π/4 rads) = -1.414 tan (3π/4 rads) = -1 cot (3π/4 rads) = -1 sin (11π/6 rads) = -0.5 csc (11π/6 rads) = -2 cos(11π/6 rads) = 0.866 sec(11π/6 rads) = 1.155 tan (11π/6 rads) = -0.577 cot (11π/6 rads) = -1.732