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 In this topic, students first distinguish between discrete and continuous random variables and then focus on probability distributions for discrete random variables. In the early lessons of this...

 Student Outcomes Students apply the law of sines or the law of cosines to determine missing measurements in realworld situations that can be modeled using nonright triangles, including situations...

 Student Outcomes Students prove the law of cosines and use it to solve problems.

 Student Outcomes Students prove the law of sines and use it to solve problems.

 Student Outcomes Students prove the formula Area = 1/2 bc sin(A) for a triangle. They reason geometrically and numerically to find the areas of various triangles.

 Students derive sophisticated applications of the trigonometric functions in Topic B including: the area formula for a general triangle, the law of sines, the law of cosines, and Heron’s formula. ...

 This module revisits trigonometry that was introduced in Geometry and Algebra II, uniting and further expanding the ideas of right triangle trigonometry and the unit circle. New tools are introduced...

 Student Outcomes Students develop an understanding of how to determine a missing angle in a right triangle diagram and applythis to real world situations.

 Student Outcomes Students understand that the Law of Sines can be used to find missing side lengths in a triangle when you know the measures of the angles and one side length. Students understand...

 Student Outcomes Students find missing side lengths of an acute triangle given one side length and the measures of two angles. Students find the missing side length of an acute triangle given two...

 Student Outcomes Students prove that the area of a triangle is onehalf times the product of two side lengths times the sine of the included angle and solve problems using this formula. Students find...

 Student Outcomes Students rewrite the Pythagorean Theorem in terms of sine and cosine ratios, and use it in this form to solve problems. Students write tangent as an identity in terms of sine and...

 Student Outcomes Students understand that the value of the tangent ratio of the angle of elevation or depression of a line is equal to the slope of the line. Students use the value of the tangent...

 Student Outcomes Students use graphing calculator to find the values of sin θ and cos θ for θ between 0 and 90. Students solve for missing sides of a right triangle given the length of one side and...

 Student Outcomes Students understand that if α and β are the measurements of complementary angles, then sin α=cos β. Students solve triangle problems using special angles.

 It is convenient, as adults, to use the notation “ ” to refer to the value of the square of the sine function. However, rushing too fast to this abbreviated notation for trigonometric functions...

 In Lesson 26, students discover that the values of the and ratios in a right triangle depend solely on the measure of the acute angle by which the adjacent, opposite, and hypotenuse sides are...

 Students link their understanding of similarity and relationships within similar right triangles formally to trigonometry. In addition to the terms sine, cosine, and tangent, students study the...

 Student Outcomes Students prove the Pythagorean Theorem using similarity. Students use similarity and the Pythagorean Theorem to find the unknown side lengths of a right triangle. Students are...

 Student Outcomes Students use the distributive property to simplify expressions that contain radicals.

 Student Outcomes Students multiply and divide expressions that contain radicals to simplify their answers. Students rationalize the denominator of a number expressed as a fraction.

 Student Outcomes Students understand that the altitude of a right triangle from the vertex of the right angle to the hypotenuse divides the triangle into two similar right triangles that are also...

 The focus in Topic D is similarity within right triangles. Students examine how an altitude drawn from the vertex of a right triangle to the hypotenuse creates two similar subtriangles. Students...

 Student Outcomes Students state, understand, and prove the Angle Bisector Theorem. Students use the Angle Bisector Theorem to solve problems.