Basic Trig

Essential Question: How can you find the length of a side of a triangle or the measure of any angle?

Angles

1) Measuring an Angle with Degrees, Minutes, and Seconds

Basic Trig

2) Introduction to Trig Ratios

3) Trig Ratios with Pythagorean Theorem

4) Inverse Trig Ratios

5) Solve for missing sides & angles in a right triangle

6) Relationship of sides and angles in a right triangle

7) Indirect Measurements in a right triangle

8) Indirect Measurement with unknowns sides

9) Law of Sines (for triangles that are not right)

10) Law of Cosines (for triangles that are not right)

11) Review using trig with triangles

12) Navigation

13a) Vectors - Basics

13b) Vectors: format conversion and addition/subtraction:

14) Trig and Area

15) Review

Common Core Standard: Geometry: Similarity, Right Triangles, and Trig

Define trigonometric ratios and solve problems involving right triangles:

  • C.6: Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
  • C.7: Explain and use the relationship between the sine and cosine of complementary angles.
  • C. 8: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

Define trigonometric ratios and solve problems involving right triangles:

  • D.9: Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.
  • D.10: Prove the Laws of Sines and Cosines and use them to solve problems.
  • D.11: Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces).