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Use what you know about trigonometric identities to explore the questions below. 1. Amna needs to decide if the equation values for 0, substitute them into this equation, and simplify. What do your results indicate about the equation =1- cos e is an identity. Choose 3 possible sine 1+cose =1- cos e? Show all your work.

Use what you know about trigonometric identities to explore the questions below. 1. Amna needs to decide if the equation values for 0, substitute them into this equation, and simplify. What do your results indicate about the equation =1- cos e is an identity. Choose 3 possible sine 1+cose =1- cos e? Show all your work.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Module 11, Triqonometric Identities Assiqnment In mathematics, an identity is an equation that is always true. When you learned how to factor expressions and equations, you worked with several algebraic identities, including (a + b)? = a? + 2ab + b? and (a – b) = (a – b)(a² + ab + b²). These identities helped you to rewrite and simplify more complex expressions or equations. This, in tum, allowed you to more easily solve problems. In this module you were introduced to trigonometric identities, including reciprocal identities, quotient identities, Pythagorean identities, and others. Like algebraic identities, you can use trigonometric identities to help you rewrite and simplify more complex expressions or equations in order to more easily solve problems. You can also use these identities to verify whether trigonometric equations represent identities. There are several ways to show an cquation may be an identity, but to prove it is an identity, you must verify it. Use what you know about trigonometric identities to explore the questions below. 1. Amna needs to decide if the equationcose values for 0, substitute them into this equation, and simplify. What do your results indicate about the equation cas e sine ;=1- cos e is an identity. Choose 3 possible sin?e = 1- cos 8? Show all your work. 2. The graphs of- sin e ,in red, and 1- cos 8, in blue, are shown below. What do these graphs 1+cose sine and your answer to question 1 indicate about the equation = 1- cos 0? Explain. 1+cose
Transcribed Image Text:Module 11, Triqonometric Identities Assiqnment In mathematics, an identity is an equation that is always true. When you learned how to factor expressions and equations, you worked with several algebraic identities, including (a + b)? = a? + 2ab + b? and (a – b) = (a – b)(a² + ab + b²). These identities helped you to rewrite and simplify more complex expressions or equations. This, in tum, allowed you to more easily solve problems. In this module you were introduced to trigonometric identities, including reciprocal identities, quotient identities, Pythagorean identities, and others. Like algebraic identities, you can use trigonometric identities to help you rewrite and simplify more complex expressions or equations in order to more easily solve problems. You can also use these identities to verify whether trigonometric equations represent identities. There are several ways to show an cquation may be an identity, but to prove it is an identity, you must verify it. Use what you know about trigonometric identities to explore the questions below. 1. Amna needs to decide if the equationcose values for 0, substitute them into this equation, and simplify. What do your results indicate about the equation cas e sine ;=1- cos e is an identity. Choose 3 possible sin?e = 1- cos 8? Show all your work. 2. The graphs of- sin e ,in red, and 1- cos 8, in blue, are shown below. What do these graphs 1+cose sine and your answer to question 1 indicate about the equation = 1- cos 0? Explain. 1+cose
3. If possible, verify cos e match the right-hand side of the cquation. Show all your steps. If not possible, explain why. sine ;=1- cos e is true by rewriting the left-hand side of the equation to 4. If possible, algebraically verif - sine =1- cos e in a different way. Show all your steps. If 1+cos e not possible, explain why. 5. Is the equation cos 8 - sine = 1 an identity? If so, verify it. If not, explain why.
Transcribed Image Text:3. If possible, verify cos e match the right-hand side of the cquation. Show all your steps. If not possible, explain why. sine ;=1- cos e is true by rewriting the left-hand side of the equation to 4. If possible, algebraically verif - sine =1- cos e in a different way. Show all your steps. If 1+cos e not possible, explain why. 5. Is the equation cos 8 - sine = 1 an identity? If so, verify it. If not, explain why.
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