
Understanding Half Angle Identities and Power Reducing Formulas

Interactive Video
•
Mathematics
•
9th - 12th Grade
•
Hard
Standards-aligned

Olivia Brooks
FREE Resource
Standards-aligned
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the main goal of the problem discussed in the video?
To find the exact value of cos(112.5°) using a reference triangle.
To find the exact value of sin(112.5°) using a half angle identity.
To determine the cosine of 112.5° using a unit circle.
To calculate the tangent of 112.5° using trigonometric identities.
Tags
CCSS.HSF.TF.C.9
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Which identity is used to express sin^2(a) in terms of cosine?
sin^2(a) = 1 + sin(2a)
sin^2(a) = 1 - cos^2(a)
sin^2(a) = 1 + cos(2a)
sin^2(a) = 1 - cos(2a)
Tags
CCSS.HSF.TF.A.2
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How is the cosine of 225° determined in the video?
By using the sine function.
By applying the Pythagorean theorem.
By sketching a reference triangle and using the unit circle.
Using a calculator.
Tags
CCSS.HSF.TF.A.2
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the cosine of 225° as found in the video?
√2/2
1/2
-√2/2
-1/2
Tags
CCSS.HSF.TF.A.2
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the purpose of using a reference triangle in trigonometry?
To determine the sine and cosine of angles using known ratios.
To calculate the tangent of angles.
To simplify complex trigonometric expressions.
To find the exact value of angles.
Tags
CCSS.HSF.TF.A.2
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In which quadrant does the angle 112.5° lie?
Second quadrant
First quadrant
Fourth quadrant
Third quadrant
Tags
CCSS.HSF.TF.A.2
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Why is the sine of 112.5° positive?
Because it lies in the third quadrant.
Because it lies in the first quadrant.
Because it lies in the fourth quadrant.
Because it lies in the second quadrant where y-coordinates are positive.
Tags
CCSS.HSF.TF.C.9
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