- Common endpoint of two rays that form the angle. Other Lesson 3 Applying the CAST Rule STAGE 1 BIG IDEA: The sine law and cosine law allows us to work with non right triangles. Applications of trigonometry include surveying, navigation, construction, and calculus. ENDURING UNDERSTANDINGS: ESSENTIAL QUESTIONS: Students will understand What is triangulation? … How many different ways can you estimate Angles in a circle can be expressed in a the height of a mountain? variety of ways. Why is it easier to find the exact value of Each primary trigonometric ratio is positive in some trigonometric ratios? two quadrants and negative in two quadrants between 0o and 360o (CAST). KNOWLEDGE: SKILLS: Students will be able to … Students will know … determine the value of sin cos or tan θ, θ θ, the sign of a given trigonometric ratio for a given any point P (x, y) on the terminal arm of given angle, without the use of technology, angle θ and explain determine, without the use of technology, the the exact value of the sine, cosine or tangent value of sin cos or tan given any point θ, θ θ, of a given angle with a reference angle of 30º, P (x, y) on the terminal arm of angle where θ, 45º or 60º = 0º, 90º, 180º, 270º or 360º θ the patterns in and among the values of the determine the sign of a given trigonometric sine, cosine and tangent ratios for angles from ratio for a given angle, without the use of 0° to 360° technology, and explain some contextual problems can be solved solve, for all values of an equation of the using trigonometric ratios θ, form sin = a or cos = a, where a 1, θ θ −1 ≤ ≤ and an equation of the form tan = a, where a θ is a real number determine the exact value of the sine, cosine or tangent of a given angle with a reference angle of 30º, 45º or 60º describe patterns in and among the values of the sine, cosine and tangent ratios for angles from 0° to 360° solve a contextual problem, using trigonometric ratios Lesson Summary
- Common endpoint of two rays that form the angle. Other Lesson 3 Applying the CAST Rule STAGE 1 BIG IDEA: The sine law and cosine law allows us to work with non right triangles. Applications of trigonometry include surveying, navigation, construction, and calculus. ENDURING UNDERSTANDINGS: Students will understand … Angles in a circle can be expressed in a variety of ways. Each primary trigonometric ratio is positive in two quadrants and negative in two quadrants between 0o and 360o (CAST). ESSENTIAL QUESTIONS: What is triangulation? How many different ways can you estimate the height of a mountain? Why is it easier to find the exact value of some trigonometric ratios? KNOWLEDGE: Students will know … the sign of a given trigonometric ratio for a given angle, without the use of technology, and explain the exact value of the sine, cosine or tangent of a given angle with a reference angle of 30º, 45º or 60º the patterns in and among the values of the sine, cosine and tangent ratios for angles from 0° to 360° some contextual problems can be solved using trigonometric ratios SKILLS: Students will be able to … determine the value of sin θ, cos θ or tan θ, given any point P (x, y) on the terminal arm of angle θ determine, without the use of technology, the value of sin θ, cos θ or tan θ, given any point P (x, y) on the terminal arm of angle θ, where θ = 0º, 90º, 180º, 270º or 360º determine the sign of a given trigonometric ratio for a given angle, without the use of technology, and explain solve, for all values of θ, an equation of the form sin θ = a or cos θ = a, where −1 ≤ a ≤ 1, and an equation of the form tan θ = a, where a is a real number determine the exact value of the sine, cosine or tangent of a given angle with a reference angle of 30º, 45º or 60º describe patterns in and among the values of the sine, cosine and tangent ratios for angles from 0° to 360° solve a contextual problem, using trigonometric ratios Lesson Summary