
Understanding Derivatives of Inverse Trigonometric Functions

Interactive Video
•
Mathematics
•
10th - 12th Grade
•
Hard
Standards-aligned

Ethan Morris
FREE Resource
Standards-aligned
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the derivative of the inverse sine of x?
1 over the square root of 1 minus x squared
Negative 1 over the square root of 1 minus x squared
1 over 1 plus x squared
Negative 1 over 1 plus x squared
Tags
CCSS.HSF-BF.B.4A
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the first step in finding the derivative of the inverse cosine of x?
Use the Pythagorean identity
Differentiate x with respect to y
Set y equal to the inverse cosine of x
Set y equal to the inverse sine of x
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
When differentiating x = cos(y), what is the derivative of cos(y) with respect to y?
sin(y)
Negative cos(y)
Negative sin(y)
cos(y)
Tags
CCSS.HSF.TF.B.7
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How do you express dy/dx in terms of x after finding it in terms of y?
Use the identity sin(y) = 1 - cos^2(y)
Use the identity tan^2(y) + 1 = sec^2(y)
Use the identity 1 + cot^2(y) = csc^2(y)
Use the identity sin^2(y) + cos^2(y) = 1
Tags
CCSS.HSF-BF.B.4A
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the derivative of the inverse cosine of x?
1 over the square root of 1 minus x squared
Negative 1 over the square root of 1 minus x squared
1 over 1 plus x squared
Negative 1 over 1 plus x squared
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Which trigonometric identity is used to convert dy/dx from terms of y to terms of x?
sin^2(y) + cos^2(y) = 1
tan^2(y) + 1 = sec^2(y)
sin(y) = 1 - cos^2(y)
1 + cot^2(y) = csc^2(y)
Tags
CCSS.HSF.TF.C.8
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the expression for sine of y in terms of cosine of y?
Square root of 1 minus cosine squared of y
Square root of 1 plus cosine squared of y
1 plus cosine squared of y
1 minus cosine squared of y
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