As a demonstration, draw a Cartesian plane, choose a point in quadrant I, and draw a terminal arm through the point. Determine: distance from the origin to the point the exact value of the sin cos and tan θ, θ, θ the reference angle Student Pairs Activity: Students pick any point in quadrant I and draw a terminal arm. Students should then swap papers and determine: distance from the origin to the point the exact value of the sin cos and tan θ, θ, θ the reference angle Going Beyond Continue the above lesson using negative angles and angles beyond 360 Resources Math 20-1 (McGraw-Hill Ryerson: sec 2.2, pages 88-99) source: Supporting Assessment Glossary angle in standard position - The location of an angle in the plane in which the vertex is at the origin, the initial arm lies along the positive x-axis, and the terminal arm is free to rotate initial arm - For an angle in standard position, the arm along the positive x-axis quadrantal angle an angle in standard position where the terminal arm is on the x- or – Examples are 0°, 90°, 180°, 270° and 360°. reference angle The acute angle formed by the terminal arm of an angle in standard – position and the x-axis rotation angles: positive angle - An angle in standard position swept out by a counterclockwise rotation of its terminal arm negative angle - An angle in standard position swept out by a clockwise rotation of its terminal arm reference triangle A right triangle with a reference angle as one of its vertices – terminal arm For an angle in standard position, the arm that is free to rotate –
As a demonstration, draw a Cartesian plane, choose a point in quadrant I, and draw a terminal arm through the point. Determine: distance from the origin to the point the exact value of the sin θ, cos θ, and tan θ the reference angle Student Pairs Activity: Students pick any point in quadrant I and draw a terminal arm. Students should then swap papers and determine: distance from the origin to the point the exact value of the sin θ, cos θ, and tan θ the reference angle Going Beyond Continue the above lesson using negative angles and angles beyond 360 Resources Math 20-1 (McGraw-Hill Ryerson: sec 2.2, pages 88-99) source: Supporting Assessment Glossary angle in standard position - The location of an angle in the plane in which the vertex is at the origin, the initial arm lies along the positive x-axis, and the terminal arm is free to rotate initial arm - For an angle in standard position, the arm along the positive x-axis quadrantal angle – an angle in standard position where the terminal arm is on the x- or Examples are 0°, 90°, 180°, 270° and 360°. reference angle – The acute angle formed by the terminal arm of an angle in standard position and the x-axis rotation angles: positive angle - An angle in standard position swept out by a counterclockwise rotation of its terminal arm negative angle - An angle in standard position swept out by a clockwise rotation of its terminal arm reference triangle – A right triangle with a reference angle as one of its vertices terminal arm – For an angle in standard position, the arm that is free to rotate