Trigonometry

PC.FT.1Understand that the radian measure of an angle is the length of the arc on the unit circle subtended by the angle.PC.FT.2Define sine and cosine as functions of the radian measure of an angle in terms of the x- and y-coordinates of the point on the unit circle corresponding to that angle and explain how these definitions are extensions of the right triangle definitions.PC.FT.2aDefine the tangent, cotangent, secant, and cosecant functions as ratios involving sine and cosine.PC.FT.2bWrite cotangent, secant, and cosecant functions as the reciprocals of tangent, cosine, and sine, respectively.PC.FT.3Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4, and π/6, and 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 values for x, where x is any real number.PC.FT.4Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.PC.FT.5Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.PC.FT.6Define the six inverse trigonometric functions using domain restrictions for regions where the function is always increasing or always decreasing.PC.FT.7Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context.PC.FT.8Justify the Pythagorean, even/odd, and cofunction identities for sine and cosine using their unit circle definitions and symmetries of the unit circle and use the Pythagorean identity to find sin A, cos A, or tan A, given sin A, cos A, or tan A, and the quadrant of the angle.PC.FT.9Justify the sum and difference formulas for sine, cosine, and tangent and use them to solve problems.
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