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Pearson Algebra 2 Common Core, 2011

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Pearson Algebra 2 Common Core, 2011 View details

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Exercise 1 Page 963

Recall the Trigonometric Identities. Start by using the Cotangent Identity cot θ = cos θsin θ.

csc θ

Practice makes perfect

At first, let's recall the Cotangent Identity. cot θ =cos θ/sin θ With this identity, we can substitute cos θsin θ for cot θ in our expression.

sin θ +cos θ cot θ

cot θ= cos θ/sin θ

sin θ +cos θ * cos θ/sin θ

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a*b/c= a* b/c

sin θ + cos^2 θ/sin θ

a = sin θ* a/sin θ

sin^2 θ/sin θ + cos^2 θ/sin θ

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sin^2 θ + cos^2 θ/sin θ

Now we will use one of the Pythagorean Identities. sin^2 θ + cos^2 θ = 1 With this identity, we can substitute 1 for sin^2 θ + cos^2 θ in our expression.

sin^2 θ + cos^2 θ/sin θ

sin^2 θ + cos^2 θ= 1

1/sin θ

Finally, let's apply one of the Reciprocal Identities. csc θ = 1/sin θ With this identity, we can substitute csc θ for 1sin θ in our expression.

1/sin θ

1/sin θ= csc θ

csc θ

We have simplified the given expression. sin θ +cos θ cot θ = csc θ

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Exercises p.963