Trigonometry

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Trigonometry Foundations

Revisit the foundational knowledge of linear measurement in algebra and angular measurement in geometry to apply to trigonometry. Learn a new, more natural angular measurement system: radians. Trigonometry frequently uses both measurements, so learn to convert fluidly between them in this theme. Discover the unit circle and how when combined with triangles they encompass trigonometry. Discover trigonometric functions ($\sin\theta, \cos\theta, \tan\theta$) and their reciprocal functions for use in analyzing angle measures.

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The Rectangular Coordinate SystemFree

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Angles, Degrees, and Radians

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The Unit Circle

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Trigonometric Functions

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Trigonometric Identities

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Reciprocal Trigonometric Functions

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Right Angle Trigonometry

Behold the basis of trigonometry. Revisit right triangle attributes and calculations, and apply sines and cosines with the unit circle. Apply angle measures, Pythagorean Theorem, and SOH CAH TOA.

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Your status is based on your weighted accuracy which accounts for the difficulty of the questions.

Your weighted accuracy is based on your most recent attempts compared to everyone else’s first attempts.

Re-answering questions correctly will improve your weighted average status.

Acute Angles

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Solving Right Triangles

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Trigonometric Functions of Common Angles

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Trigonometric Functions of Complementary Angles

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Applications

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Elevation and depression

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Vectors

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Navigation

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Triangles

Apply trigonometric functions to non-right triangles using the Law of Sines and Law of Cosines to solve for missing side lengths or angles. Practice finding area of non-right triangles, occasionally using these laws.

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Accuracy is based on your most recent attempt.

Status

Your status is based on your weighted accuracy which accounts for the difficulty of the questions.

Your weighted accuracy is based on your most recent attempts compared to everyone else’s first attempts.

Re-answering questions correctly will improve your weighted average status.

Area

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The Law of Sines

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The Law of Cosines

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Vectors

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Radians

Use your understanding of radians and trigonometric functions to evaluate the following expressions using a point and angle on the unit circle. From there, apply these concepts to evaluate arc length and angular speed.

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Accuracy is based on your most recent attempt.

Status

Your status is based on your weighted accuracy which accounts for the difficulty of the questions.

Your weighted accuracy is based on your most recent attempts compared to everyone else’s first attempts.

Re-answering questions correctly will improve your weighted average status.

Point-in-the-Plane Description of Trig Functions

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Applications

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Arc length

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Angular speed

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Inverse Trigonometric Functions

Work backwards: you can find the sine and cosine values of different angles. Now use the inverse functions to find the angles given the sine and cosine values. Apply these for all the trigonometric functions and utilize them for simple physics applications involving rocketry.

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Accuracy is based on your most recent attempt.

Status

Your status is based on your weighted accuracy which accounts for the difficulty of the questions.

Your weighted accuracy is based on your most recent attempts compared to everyone else’s first attempts.

Re-answering questions correctly will improve your weighted average status.

Evaluating Inverse Trignometric Functions

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Equations with Inverse Trigonemtric Functions

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Graphing Trignometric Functions

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Your status is based on your weighted accuracy which accounts for the difficulty of the questions.

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Basics of Graphing

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Amplitude

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Period

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Reflection

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Finding Equations From Graphs

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Analytic Trigonometry

Continue developing your trigonometry knowledge through use of trigonometric identities. Use the identities to simplify complex expressions and solve for unknowns through equations.

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Accuracy is based on your most recent attempt.

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Your status is based on your weighted accuracy which accounts for the difficulty of the questions.

Your weighted accuracy is based on your most recent attempts compared to everyone else’s first attempts.

Re-answering questions correctly will improve your weighted average status.

Trigonometry with Multiple Angles

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Trigonometric Identities

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Proving identities

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Solving equations

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Formulas

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Sum and difference formulas

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Double-angle formulas

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Half-angle formulas

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Complex Numbers

Evaluate complex trigonometric equations and annotate them in standard complex form. Perform operations with and change forms of complex numbers.

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Accuracy is based on your most recent attempt.

Status

Your status is based on your weighted accuracy which accounts for the difficulty of the questions.

Your weighted accuracy is based on your most recent attempts compared to everyone else’s first attempts.

Re-answering questions correctly will improve your weighted average status.

Introduction to Complex Numbers

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Trigonometric Form of Complex Numbers

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Polar Form

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Polar coordinates

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Trigonometric functions

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De Moivre's Theorem

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