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
Explanation:
Practice Problems:
Basic Trig
2) Introduction to Trig Ratios
Explanation:
Khan article: Hypotenuse, opposite, and adjacent
Khan video: Intro to the trigonometric ratios
Khan article: Trigonometric ratios in right triangles
Khan article: Reciprocal trig ratios
Khan video: Finding reciprocal trig ratios
Khan article: Trigonometric ratios review
Practice Problems:
Khan Exercise: Trigonometric ratios in right triangles
Khan Exercise: Reciprocal Trig Functions
Quizlet Flashcards: Trig Ratios
3) Trig Ratios with Pythagorean Theorem
Explanation:
Khan video: Trigonometric ratios in right triangles
Khan video: Using reciprocal trig ratios
Practice:
4) Inverse Trig Ratios
Explanation:
Khan article: Intro to inverse trig functions
Practice Problems:
Khan exercise: Solve for an angle in right triangles
5) Solve for missing sides & angles in a right triangle
Explanation:
Practice Problems:
Khan exercise: Solve for a side in right triangles
6) Relationship of sides and angles in a right triangle
Explanation:
Khan article: Sine & cosine of complementary angles
Khan video: Sine & cosine of complementary angles
Khan video: Using complementary angles
Practice Problems:
7) Indirect Measurements in a right triangle
Explanation:
Khan video: Right triangle word problem
Khan article: Angles of elevation and depression
Khan article: Right triangle trigonometry review
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Practice Problems:
Khan Exercise: Right triangle word problems
Angle of Elevation and Depression: Worksheet #1 | Answers
Angle of Elevation and Depression: Worksheet #2 | Answers
8) Indirect Measurement with unknowns sides
Explanation
Practice Problems
9) Law of Sines (for triangles that are not right)
Explanation:
Given two sides and a non-included angle (non-ambiguous case): Notes | Annotated
Honors: Given two sides and a non-included angle (ambiguous case): Notes | Annotated
Khan video: Solving for a side with the law of sines
Khan video: Solving for an angle with the law of sines
Khan video: Proof of the law of sines
Practice Problems
Khan exercise: Solve triangles using the law of sines
10) Law of Cosines (for triangles that are not right)
Explanation:
Khan video: Solving for a side with the law of cosines
Khan video: Solving for an angle with the law of cosines
Khan video: Proof of the law of cosines
Practice Problems
11) Review using trig with triangles
Explanation
Khan video: Trig word problem: stars
Khan article: Laws of sines and cosines review
Practice Problems:
12) Navigation
13a) Vectors - Basics
Explanation:
Khan video: Equivalent vectors
Khan video: Components of vectors
Khan video: Components of vectors (example 2)
Khan video: Vector magnitude from graph
Khan video: Vector magnitude from components
Khan video: Vector magnitude from initial & terminal points
Khan video: Scalar multiplication of vectors
Khan video: Adding & subtracting vectors
Khan video: Combined vector operations
Practice Problems:
Khan Exercise: Equivalent vectors
Khan Exercise: Components of vectors
Khan Exercise: Magnitude of vectors
Khan Exercise: Scalar multiplication
Khan Exercise: Add & subtract vectors
Khan Exercise: Combined vector operations
Interactive game: Vector Investigation – Boat to Island
13b) Vectors: format conversion and addition/subtraction:
Explanation:
Khan video: Unit vectors intro
Khan video: Direction of vectors from components: 1st & 2nd quadrants
Khan video: Direction of vectors from components: 3rd & 4th quadrants
Khan article: Vector forms review
Khan video: Vector components from magnitude & direction
Khan article: Vector components from magnitude & direction (advanced)
Khan article: Vector magnitude and direction review
Khan video: Vectors word problem: pushing a box
Khan video: Vectors word problem: hiking
Practice Problems:
Khan exercise: Direction of vectors
Khan exercise: Vector components from magnitude & direction
Khan exercise: Add vectors: magnitude & direction to component
Khan exercise: Add vectors: magnitude & direction
Khan exercise: Vector word problems
14) Trig and Area
Explanation
Notes | Annotated
Practice Problems
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).