T.3.PC

T.3.PC

T.3.PC.1Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.T.3.PC.2Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed around the unit circle.T.3.PC.3(+) Use special right triangles to determine geometrically the exact values of sine, cosine, tangent for π/3, π/4, π/6, and π/2. (+) Use the unit circle to express the values of sine, cosine, and tangent for π-x, π+x, and 2π-x in terms of their exact values for x where x is any real number.T.3.PC.4(+) Develop the Pythagorean identity, sin^2(θ) + cos^2(θ) = 1. (+) Given sin(θ) , cos(θ), or tan(θ) and the quadrant of the angle, use the Pythagorean identity to find the remaining trigonometric functions.T.3.PC.5(+) Develop the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.T.3.PC.6Derive the formula A = (½)ab sin C for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.T.3.PC.7Prove the Law of Sines and the Law of Cosines and use them to solve problems.T.3.PC.8(+) Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles.T.3.PC.9Define and use reciprocal functions, cosecant, secant, and cotangent to solve problems.
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