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MAP 4C Name: _______________ EXPLORING TRIGONOMETRIC RATIOS ACTIVITY THINGS YOU NEED TO KNOW BEFORE STARTING! Quadrants Angles Angles in triangles are named using the corners, for example: CAB The letter of the angle is the one in the middle MAP 4C Name: _______________ 1. Under ‘My Computer’ choose ‘Students Common’, ‘Pickup’, ‘Carew’, ‘MAP 4C’, ‘Investigating Sin, Cos, Tan of Angles.gsp’. The screen should show: Save this to your H drive. 2. Choose a point for C in Quadrant 1, so that ABC is a right angle triangle. What is the measure of angle A? a) Which side is opposite angle A? b) Which side is adjacent to angle A? c) Which side is the hypotenuse? d) Complete the following chart: Calculator Answer Sin A = Cos A = Tan A = 3. Move point C around Quadrants 1 and 2. a) Which type of angle is A if C is in Quadrant 1? b) Which type of angle is A if C is in Quadrant 2? Fraction to a Decimal MAP 4C Name: _______________ 4. Choose a point for C in Quadrant 2, so that AEC is a right angle triangle. a) Is the x-coordinate of C positive or negative? b) Is the y-coordinate of C positive or negative? 5. a) When angle A is acute, state the signs for the x and y values. x: y: b) When angle A is obtuse, state the signs for the x and y values. x: y: 6. Suppose angle A is acute. Use your answers from # 5 to help you answer the following questions: a) Think about sin 𝐴 = b) Think about cos 𝐴 = c) Think about tan 𝐴 = 𝑂𝑝𝑝 𝐻𝑦𝑝 . Is sin A positive or negative? Explain why. 𝐴𝑑𝑗 𝐻𝑦𝑝 𝑂𝑝𝑝 𝐴𝑑𝑗 . Is cos A positive or negative? Explain why. . Is tan A positive or negative? Explain why. MAP 4C Name: _______________ 7. Suppose angle A is obtuse. Use your answers from # 5 to help you answer the following questions: a) Think about sin 𝐴 = b) Think about cos 𝐴 = c) Think about tan 𝐴 = 𝑂𝑝𝑝 𝐻𝑦𝑝 . Is sin A positive or negative? Explain why. 𝐴𝑑𝑗 𝐻𝑦𝑝 . Is cos A positive or negative? Explain why. 𝑂𝑝𝑝 𝐴𝑑𝑗 . Is tan A positive or negative? Explain why. 8. Use a calculator to complete the table below. Round your answer to 4 decimal places. Use the straight line to get the Angle Measure of Acute Angle A. Angle Measure Sin A Cos A Tan A Acute Angle A Obtuse Angle A How do your answers to # 6 and # 7 compare to your answers in the table? 9. Use your answers to # 8 and # 9 to complete the table on your formula sheet.