Trigonometric equations and identities
10 videos
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Trigonometry - Trig Equations & Identities: What You Need to Know
Learn inverse trig functions, solving sinusoidal equations, and angle addition identities. Master moving between angles and ratios in both directions.
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Trigonometry - Inverse Trig Functions: Arcsine, Arccosine, Arctangent
Learn how inverse trig functions work by taking ratios and returning angles within specific principal value ranges to ensure unique outputs.
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Trigonometry - Evaluating Inverse Trig Functions
Learn how to find principal values of inverse trig functions by understanding restricted ranges. Example shows why arcsin(√3/2) = π/3, not 2π/3.
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Trigonometry - Solving Trig Equations: Finding ALL Solutions
Learn how to find all solutions to trig equations using the unit circle and period 2πn. Covers cosine equations and common mistakes to avoid.
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Trigonometry - Solving a Sinusoidal Equation Step by Step
Learn how to solve sinusoidal equations step-by-step, including isolating sine, using the unit circle, and finding all solutions with the correct period.
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Trigonometry - Sinusoidal Word Problem: When Does It Hit That Value?
Learn to solve sinusoidal word problems using a Ferris wheel example. Find when height reaches 55 feet by solving trigonometric equations and interpreting solutions in context.
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Trigonometry - Angle Addition Identities: sin(a+b) and cos(a+b)
Learn the sine and cosine addition formulas to find exact trig values for angles like 75°. Understand the patterns and how to apply them to derive other identities.
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Trigonometry - Finding Exact Trig Values with Angle Addition
Learn how to find exact trigonometric values using angle addition identities by splitting unfamiliar angles into known special triangle angles.
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Trigonometry - Double Angle Identities: cos(2θ) and sin(2θ)
Learn how to derive and use double angle identities for sine and cosine from angle addition formulas, including three forms of the cosine double angle identity.
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Trigonometry - Simplifying Expressions with Trig Identities
Learn how two key trig identities—Pythagorean and quotient—can simplify complex expressions. Step-by-step example shows how to recognize and apply them effectively.