Understanding Trigonometric Functions: Domain and Range

The video tutorial explains the domain and range of three trigonometric functions: sine, cosine, and tangent. It begins with an introduction to these functions using a unit circle. The domain of sine and cosine is all real numbers, while the domain of tangent excludes values where cosine is zero. The range of sine and cosine is between -1 and 1, and the range of tangent is from negative to positive infinity. The tutorial uses visual aids and mathematical reasoning to clarify these concepts.

What is the primary tool used to understand the domain and range of trigonometric functions in this lesson?

• A protractor

• A graphing calculator

• A unit circle

• A number line

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CCSS.HSF.TF.A.2

For sine and cosine functions, what is the domain of theta?

• All real numbers

• Only even numbers

• Only negative integers

• Only positive integers

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CCSS.HSF.TF.A.2

Why do sine and cosine functions have no restrictions on their domain?

• Because theta appears in the numerator

• Because theta does not appear in the denominator

• Because theta is always zero

• Because theta is always positive

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CCSS.HSF.TF.A.2

What condition causes the tangent function to have restrictions in its domain?

• When theta is a multiple of 360 degrees

• When sine theta is zero

• When cosine theta is zero

• When theta is a multiple of 180 degrees

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CCSS.HSF.TF.A.2

At which angles is cosine theta zero, affecting the domain of tangent?

• 0 and 180 degrees

• 90 and 270 degrees

• 45 and 225 degrees

• 60 and 300 degrees

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CCSS.HSF.TF.A.2

What is the range of values for cosine theta?

• Between -1 and 1

• Between -2 and 2

• Between 0 and 2

• Between -0.5 and 0.5

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CCSS.HSF.TF.A.4

What is the range of values for sine theta?

• Between -0.5 and 0.5

• Between -1 and 1

• Between 0 and 2

• Between -2 and 2

What is the range of the tangent function?

• Between -1 and 1

• Between -infinity and infinity

• Between 0 and 1

• Between -2 and 2

When is the tangent function considered to be at its maximum value?

• When sine theta is 0 and cosine theta is 1

• When sine theta is 1 and cosine theta is 0

• When sine theta is -1 and cosine theta is 0

• When sine theta is 0 and cosine theta is -1

When is the tangent function considered to be at its minimum value?

• When sine theta is -1 and cosine theta is 0

• When sine theta is 1 and cosine theta is 0

• When sine theta is 0 and cosine theta is -1

• When sine theta is 0 and cosine theta is 1