Which identity is used to express cosine squared theta in terms of sine squared theta?

Integrals Involving Trigonometric Substitutions

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Mathematics
•
10th - 12th Grade
•
Hard

Amelia Wright
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10 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
sec^2(theta) - 1 = tan^2(theta)
1 + tan^2(theta) = sec^2(theta)
sin^2(theta) + cos^2(theta) = 1
1 - sin^2(theta) = cos^2(theta)
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
For the integral involving the square root of a^2 - x^2, what substitution is used for x?
x = a sin(theta)
x = a tan(theta)
x = a cos(theta)
x = a sec(theta)
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What does the square root of a^2 - x^2 simplify to when x = a sin(theta)?
a cos(theta)
a sin(theta)
a sec(theta)
a tan(theta)
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
For the integral involving the square root of a^2 + x^2, what substitution is used for x?
x = a cos(theta)
x = a tan(theta)
x = a sin(theta)
x = a sec(theta)
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What does the square root of a^2 + x^2 simplify to when x = a tan(theta)?
a tan(theta)
a sec(theta)
a cos(theta)
a sin(theta)
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
For the integral involving the square root of x^2 - a^2, what substitution is used for x?
x = a cos(theta)
x = a tan(theta)
x = a sec(theta)
x = a sin(theta)
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What does the square root of x^2 - a^2 simplify to when x = a sec(theta)?
a sin(theta)
a cos(theta)
a sec(theta)
a tan(theta)
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