Unpacked Content
Knowledge
Students know:
- Techniques to construct similar triangles.
- Properties of similar triangles.
- Methods for finding sine and cosine ratios in a right triangle (e.g., use of triangle properties: similarity. Pythagorean Theorem. isosceles and equilateral characteristics for 45-45-90 and 30-60-90 triangles and technology for others).
- Methods of using the trigonometric ratios to solve for sides or angles in a right triangle.
- The Pythagorean Theorem and its use in solving for unknown parts of a right triangle.
Skills
Students are able to:
- Accurately find the side ratios of triangles.
- Explain and justify relationships between the side ratios of a right triangle and the angles of a right triangle.
Understanding
Students understand that:
- The ratios of the sides of right triangles are dependent on the size of the angles of the triangle.
- The sine of an angle is equal to the cosine of the complement of the angle.
- Switching between using a given angle or its complement and between sine or cosine ratios may be used when solving contextual problems.
Vocabulary
- Side ratios
- Trigonometric ratios
- Sine
- Cosine
- Tangent
- Secant
- Cosecant
- Cotangent
- Complementary anglesconverse
