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 b a b a +b sin(a+ b) sina sinb sina a +sinb 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.
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 b a b a +b sin(a+ b) sina sinb sina a +sinb 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.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text: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
b
a
b
a +b
sin(a+ b)
sina
sinb
sina
a
+sinb
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:1. Suppose a fellow student claims that the equation şinla + b) = sina + 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) =
sina + sinb “is an identity"?
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