**1**Identify the unit circle as a tool for the study of trigonometry.**1.1**1.1: Investigate the history of trigonometry and its contributions to humanity.**1.2**1.2: Determine the importance of trigonometry for our surroundings.**1.3**1.3: Identify the circumference of the unit circle as a reference to measure angles, in radians, in the coordinate plane.**1.4**1.4: Place angles in the plane, with vertex at the origin and initial side on the x-axis.**1.5**Construct right triangles with vertices at the origin, a point of the unit circle, and a point on the x- or y-axis.

**2**Describe the cosine ratio.**2.1**Relate the cosine of an angle to the abscissa of any point of the unit circle.**2.2**Identify the cosine as a real number between -1 and 1.**2.3**Interpret the cosine as a ratio between the side adjacent to an angle of a right triangle and the hypotenuse.**2.4**Establish geometric arguments to interpret the cosine as a ratio between the adjacent side and the hypotenuse of a right triangle.

**3**Describe the sine ratio.**3.1**Interpret the sine of an angle as the ordinate of any point of the unit circle.**3.2**Identify the sine as a real number between -1 and 1.**3.3**Interpret the sine as a ratio between the side opposite to an angle of a right triangle and the hypotenuse.**3.4**Establish geometric arguments to interpret the sine as a ratio between the opposite side and the hypotenuse of a right triangle.

**4**Describe the tangent ratio.**4.1**Interpret the tangent as a ratio of the opposite side to the adjacent side of an angle of a right triangle.**4.2**Identify the tangent as the quotient of the sine and the cosine of a given angle.**4.3**Identify the tangent as the quotient of the ordinate and the abscissa of the coordinates of a point of the unit circle with center at the origin.**4.4**Deduce that the tangent is not limited by any value.**4.5**Establish that the tangent is undefined for certain angles.**4.6**Generalize the values of the angles for which the tangent is undefined.

**5**Describe the cotangent ratio.**5.1**Interpret the cotangent as a ratio between the adjacent side and the side opposite to an angle of a right triangle.**5.2**Identify the cotangent as the multiplicative inverse of the tangent.**5.3**Identify the cotangent as the quotient of the abscissa and the ordinate of the coordinates of a point of the unit circle with center at the origin.**5.4**Deduce that the cotangent is not limited by any value.**5.5**Establish that the cotangent is undefined for certain angles.**5.6**Generalize the values of the angles for which the cotangent is undefined.

**6**Describe the secant ratio.**6.1**Interpret the secant as a ratio of the hypotenuse of a right triangle to the side adjacent to an angle.**6.2**Identify the secant as the multiplicative inverse of the cosine ratio.**6.3**Identify the secant as the multiplicative inverse of the abscissa of the coordinates of a point of the unit circle with center at the origin.**6.4**Deduce that the secant is not limited by any value.**6.5**Establish the values of the angles for which the secant is undefined.**6.6**Generalize the values of the angles for which the secant is undefined.

**7**Describe the cosecant ratio.**7.1**Interpret the cosecant as a ratio of the hypotenuse of a right triangle to the side opposite to an angle.**7.2**Identify the cosecant as the multiplicative inverse of the sine ratio.**7.3**Identify the cosecant as the multiplicative inverse of the ordinate of the coordinates of a point of the unit circle with center at the origin.**7.4**Deduce that the cosecant is not limited by any value.**7.5**Determine that the cosecant is not defined as a value between -1 and 1.**7.6**Establish the values of the angles for which the cosecant is undefined.**7.7**Generalize the values of the angles for which the cosecant is undefined.

**8**Find trigonometric ratios for special angles.**8.1**Relate the similarity between triangles to the Pythagorean theorem, to determine the trigonometric ratios.**8.2**Identify the special angles.**8.3**Find the values of the sine and cosine ratios for 45 degree angles, using the Pythagorean and isosceles triangle theorems.**8.4**Find the values of the sine and cosine ratios for 30 degree angles, using the Pythagorean and 30-60-90 theorems.**8.5**Find the values of the sine and cosine ratios for 60 degree angles, using the Pythagorean and 30-60-90 theorems.**8.6**Find the values of tangent, cotangent, secant, and cosecant functions for special angles.**8.7**Determine and explain regularities in the calculation of trigonometric ratios in special angles.

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