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1. Suppose a fellow student alaims that the equation sin(a + b) = sin a + sinb is an identity. He's wondering if you can help because he's not sure how to verify his claim, but says. "It just seems intuitively so." Can you help this student? a. First, understand the student's claim. What does it mean to say that sin(a + b) = sin a + sin b "is an identity"? b. If you decided to try and verify the student's claim, you'd start with one side of his equation and try to manipulate that side until it looks like the other side. But, that may turn out to be a lot of unnecessary work if, in fact, the student's claim is false. So, instead, try something else. Consider a right triangle with angles a and b. Calculate the values in the chart below, using 2 (two) various values of a and b

1. Suppose a fellow student alaims that the equation sin(a + b) = sin a + sinb is an identity. He's wondering if you can help because he's not sure how to verify his claim, but says. "It just seems intuitively so." Can you help this student? a. First, understand the student's claim. What does it mean to say that sin(a + b) = sin a + sin b "is an identity"? b. If you decided to try and verify the student's claim, you'd start with one side of his equation and try to manipulate that side until it looks like the other side. But, that may turn out to be a lot of unnecessary work if, in fact, the student's claim is false. So, instead, try something else. Consider a right triangle with angles a and b. Calculate the values in the chart below, using 2 (two) various values of a and b

Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
8th Edition
ISBN:9781305652224
Author:Charles P. McKeague, Mark D. Turner
Publisher:Charles P. McKeague, Mark D. Turner
Chapter5: Identities And Formulas
Section: Chapter Questions
Problem 2GP
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a +b sin a + sin b sin( a + b) sin a sin b a c. What does your data tell you about the student's claim? Explain. d. In this example, you discovered that function notation is not distributive. Now, show the student how to write the sum identity for the sine function; that is. sin(a + b) =- Kindly show below how you arrived at the formula.
Transcribed Image Text:a +b sin a + sin b sin( a + b) sin a sin b a c. What does your data tell you about the student's claim? Explain. d. In this example, you discovered that function notation is not distributive. Now, show the student how to write the sum identity for the sine function; that is. sin(a + b) =- Kindly show below how you arrived at the formula.
When it comes to identities, don't always let your intuition be your guide. 1. Suppose a fellow student claims that the equation sin(a + b) = sin a + sin b is an identity. He's wondering if you can help because he's not sure how to verify his claim, but says, It just seems intuitively so." Can you help this student? a. First, understand the student's claim. What does it mean to say that sin(a + b) = sin a + sinb "is an identity"? b. If you decided to try and verify the student's claim, you'd start with one side of his equation and try to manipulate that side until it looks like the other side. But, that may tum out to be a lot of unnecessary work if, in fact, the student's claim is false. So, instead, try something else. Consider a right triangle with angles a and b. Calculate the values in the chart below, using 2 (two) various values of a and b
Transcribed Image Text:When it comes to identities, don't always let your intuition be your guide. 1. Suppose a fellow student claims that the equation sin(a + b) = sin a + sin b is an identity. He's wondering if you can help because he's not sure how to verify his claim, but says, It just seems intuitively so." Can you help this student? a. First, understand the student's claim. What does it mean to say that sin(a + b) = sin a + sinb "is an identity"? b. If you decided to try and verify the student's claim, you'd start with one side of his equation and try to manipulate that side until it looks like the other side. But, that may tum out to be a lot of unnecessary work if, in fact, the student's claim is false. So, instead, try something else. Consider a right triangle with angles a and b. Calculate the values in the chart below, using 2 (two) various values of a and b
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