Trigonometric Identities
Gbogbo ọrọ náà
Trigonometric identities are equations that hold for every value of the variable, not just particular solutions. They let you rewrite expressions in simpler or more useful forms, turning an apparently difficult equation into one you can solve in a few lines. Mastering them is the key to unlocking the harder trigonometry questions on your Edexcel paper.
In this topic you will work with the two foundational identities of the 4PM1 specification and learn how to deploy them to simplify expressions, prove results, and solve equations that would otherwise resist a direct approach.
Ebumnobi
- Use the identity cos^2(theta) + sin^2(theta) = 1
- Use the identity tan(theta) = sin(theta)/cos(theta)
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- Which of the following is a trigonometric identity? A) sin(theta) = 0.5 B) sin^2(theta) + cos^2(theta) = 1 C) tan(theta) = 1 D) cos(theta) = sin(theta) Answer: B
- What is tan(theta) equal to? A) cos(theta)/sin(theta) B) sin(theta) x cos(theta) C) sin(theta)/cos(theta) D) 1/sin(theta) Answer: C
- If cos(theta) = 0.6 and theta is in the first quadrant, what is sin(theta)? A) 0.4 B) 0.64 C) 0.8 D) 0.36 Answer: C
- Which expression is equivalent to 1 - sin^2(theta)? A) sin^2(theta) B) cos^2(theta) C) tan^2(theta) D) 1 Answer: B
- Simplify sin(theta)/tan(theta). A) 1 B) sin^2(theta) C) cos(theta) D) tan(theta) Answer: C
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Verifying Trigonometric Identities and Using Trigonometric Identities to Simplify Trigonometric Expressions
Verify the fundamental trigonometric identities.
"Algebra and Trigonometry: Verifying Trigonometric Identities and Using Trigonometric Identities to Simplify Trigonometric Expressions" by OpenStax, OpenStax, Rice University, licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Source: https://openstax.org/books/algebra-and-trigonometry/pages/9-1-verifying-trigonometric-identities-and-using-trigonometric-identities-to-simplify-trigonometric-expressions. Access for free at https://openstax.org/books/algebra-and-trigonometry/pages/1-introduction
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