1 Law of Sines and Law of Cosines 2: Law of Cosines Resource Type: Lessons Discipline: Mathematics Grades: Grades 9–12 Professional Commentary: Students use right triangle trigonometry and the Pythagorean theorem to develop the law of cosines. An activity sheet, discussion questions, lesson extensions, and suggestions for assessment are included.... 2 Law of Sines and Law of Cosines 1: Law of Sines Resource Type: Lessons Discipline: Mathematics Grades: Grades 9–12 Professional Commentary: Students use right triangle trigonometry to develop the law of sines. An activity sheet, discussion questions, lesson extensions, and suggestions for assessment are included.... Resource Type: Lessons Discipline: Mathematics Grades: Grades 9–12 Professional Commentary: The Law of Cosines is an extension of the Pythagorean Theorem, but seeing how –2ab cos C fits into the picture can be difficult for students. In this lesson, students who understand the Pythagorean Theorem and right triangle trigonometry will discover the Law of Cosines by exploring the areas of squares on the sides of any... Resource Type: Lessons Discipline: Mathematics Grades: Grades 11–Postsecondary Professional Commentary: Astronomers now know that the planets in our solar system travel around the Sun in roughly circular orbits. People used to believe that the Sun and other planets orbited the Earth.... Resource Type: Content Supports -- Activities and rich problems Discipline: Mathematics Grades: Grades 9–12 Professional Commentary: Students compare trigonometric ratios for a unit and non-unit circle with the goal of observing that the ratios are independent of the radius. They thus see the benefit of using a radius of one unit.... 6 Fit By Design or Design To Fit: Mechanical Drafter Designer Resource Type: Lessons Discipline: Mathematics Grades: Grades 8–12 Professional Commentary: Students use a carpenter's square and protractor to measure the sides and angles of several right triangles. To confirm their measurements, they then compute the size of selected sides and angles using (a) the Pythagorean Theorem and (b) trigonometric ratios.... 7 NAEP Assessment Item, Grade 12: Apply Trigonometry in Pyramid to Find Angle Resource Type: Assessments Discipline: Mathematics Grades: Grades 8–12 Professional Commentary: Students are asked to find a specified angle in a regular hexagonal pyramid using trigonometry. They have the option of using a calculator.... 8 Sine Law by Discovery: Direct Variation and Triangles Resource Type: Content Supports -- Activities and rich problems Discipline: Mathematics Grades: Grades 10–12 Professional Commentary: Through guided discovery, students revisit the notion of two quantities x, y being directly proportional if they are related by a constant ratio y/x = k. This concept is reviewed through applications that confirm that a graph of directly varying quantities satisfies the form y = kx.... 9 NAEP Assessment Item, Grade 12: Find the Length of a Segment in a Triangle Resource Type: Assessments Discipline: Mathematics Grades: Grades 7–12 Professional Commentary: This multi-step problem asks students to find the length of a line segment using similar triangles and simple trigonometry. This multiple-choice question is a sample test item used in grade 12 in the 1992 National Assessment of Educational Progress (see About NAEP).... 10 NAEP Assessment Item, Grade 12: Find the Length of the Side of a Triangle Resource Type: Assessments Discipline: Mathematics Grades: Grades 8–12 Professional Commentary: Students must use the sine function to find the length of a side of a right triangle. They have the option of using a calculator.... |