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### 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: Notes | Annotated website for conversion and exploring locations on a map by latitude and longitude  Practice Problems: Basic Trig 2) Introduction to Trig Ratios Explanation: Notes | AnnotatedKhan article: Hypotenuse, opposite, and adjacentKhan video: Intro to the trigonometric ratiosKhan article: Trigonometric ratios in right trianglesKhan article: Reciprocal trig ratios  Khan video: Finding reciprocal trig ratios  Practice Problems: Khan Exercise: Trigonometric ratios in right trianglesKhan Exercise: Reciprocal Trig Functions Khan article: Trigonometric ratios reviewQuizlet Flashcards: Trig Ratios 3) Trig Ratios with Pythagorean Theorem Explanation: Notes | AnnotatedKahn video: Trigonometric ratios in right trianglesKhan video: Using reciprocal trig ratiosPractice:4)  Inverse Trig Ratios Explanation: Notes | Annotated Notes Practice Problems:Worksheet  5) Solve for missing sides & angles in a right triangle Explanation: Notes | AnnotatedKhan article: Solving for a side in right triangles with trigonometryKhan video: Solving for a side in right triangles with trigonometryKhan article: Intro to inverse trig functions Practice Problems: Khan exercise: Solve for a side in right trianglesKhan exercise: Solve for an angle in right trianglesWorksheet #1 | Answers Worksheet #2 Worksheet #3 6)  Relationship of sides and angles in a right triangle Explanation:Khan Article: Sine & cosine of complementary anglesKhan video: Sine & cosine of complementary angles Khan video: Using complementary angles Practice Problems: 7) Indirect Measurements in a right triangle Explanation: Angle of Elevation and Depression: NotesKhan video: Right triangle word problemKhan article: Angles of elevation and depressionKhan article: Right triangle trigonometry reviewWebsite - "10 most dangerous landing strips in the world" Practice Problems: Angle of Elevation and Depression: Worksheet #1 | Answers Angle of Elevation and Depression: Worksheet #2 | AnswersKhan Exercise: Right triangle word problems 8) Indirect Measurement with unknowns sides Explanation Notes | Annotated Practice Problems 9) Law of Sines (for triangles that are not right) Explanation: Given two angles and a side: Notes | Annotated Given two sides and a non-included angle (non-ambiguous case): Notes | AnnotatedHonors: Given two sides and a non-included angle (ambiguous case): Notes | AnnotatedKhan video: Solving for a side with the law of sinesKhan video: Solving for an angle with the law of sinesKhan video: Proof of the law of sines Practice Problems Khan exercise: Solve triangles using the law of sinesWorksheet #1 | Answers 10) Law of Cosines (for triangles that are not right) Explanation: Khan video: Solving for a side with the law of cosinesKhan video: Solving for an angle with the law of cosinesKhan video: Proof of the law of cosines Practice Problems Khan exercise: Solve triangles using the law of cosinesLaw of cosines worksheet #1 | Answers Law of cosines worksheet #2Khan Exercise: Law of Cosines 11) Review using trig with triangles Explanation Khan video: Law of cosines for star distanceKhan article: Laws of sines and cosines review Practice Problems: 12) Navigation Explanation Notes | Annotated Notes How to use a compass: video from REI Instructions Practice Problems 13a) Vectors - BasicsExplanation:Vectors: Notes | Annotated | AnimationWebsite: Relative Velocity and Riverboat ProblemsThe Physics ClassroomVectors components act independtly of each other:Khan video: Equivalent vectorsKhan video: Components of vectorsKhan video: Components of vectors (example 2)Khan video: Vector magnitude from graphKhan video: Vector magnitude from componentsKhan video: Vector magnitude from initial & terminal pointsKhan video: Scalar multiplication of vectorsKhan video: Adding & subtracting vectorsKhan video: Combined vector operationsPractice Problems:Khan Exercise: Equivalent vectorsKhan Exercise: Components of vectorsKhan Exercise: Magnitude of vectorsKhan Exercise: Scalar multiplicationKhan Exercise: Add & subtract vectorsKhan Exercise: Combined vector operationsWorksheet #1Worksheet #2 | AnswersInteractive game: Vector Investigation – Boat to IslandVector addition interactive game13b) Vectors: format conversion and addition/subtraction:Explanation:Vectors: Notes | AnnotatedKhan video: Unit vectors introKhan video: Direction of vectors from components: 1st & 2nd quadrantsKhan video: Direction of vectors from components: 3rd & 4th quadrantsKhan article: Vector forms reviewKhan video: Vector components from magnitude & directionKhan article: Vector components from magnitude & direction (advanced)Khan article: Vector magnitude and direction reviewKhan video: Vectors word problem: pushing a boxKhan video: Vectors word problem: hikingPractice Problems:Khan exercise: Direction of vectorsKhan exercise: Vector components from magnitude & directionKhan exercise: Add vectors: magnitude & direction to componentKhan exercise: Add vectors: magnitude & directionKhan exercise: Vector word problemsWorksheet #1 | AnswersWorksheet #2 | Answers14) Trig and Area Explanation Notes | Annotatedwebsite with video Practice Problems 15) Review Common Core Standard: Geometry: Similarity, Right Triangles, and TrigDefine 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).