Share/Like This Page
Browse Questions

Common Core Standard HSF-TF.A.4 Questions

(+) Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.

You can create printable tests and worksheets from these questions on Common Core standard HSF-TF.A.4! Select one or more questions using the checkboxes above each question. Then click the add selected questions to a test button before moving to another page.

Previous Page 1 of 5 Next
Grade 11 Trigonometry CCSS: HSF-TF.A.4

This question is a part of a group with common instructions. View group »

What is the value of [math]sin(-theta) ?[/math]
  1. [math]-x_1/y_1[/math]
  2. [math]x_1/y_1[/math]
  3. [math]-y_1/x_1[/math]
  4. [math]-y_1[/math]
Grade 11 Trigonometry CCSS: HSF-TF.A.4

This question is a part of a group with common instructions. View group »

The period of a periodic function is the smallest value of [math]T[/math] such that [math]f(x+T) = f(x)[/math] for all values of [math]x[/math] in the domain of [math]f[/math]. Using the information in the previous questions, which of the following gives the best reasoning as to why the period of the sine function is [math]2pi ?[/math]
  1. Since values of [math]T[/math] less than [math]2pi[/math] weren't valid, [math]2pi[/math] must work.
  2. Using [math]T=2pi[/math] and trying a few values of [math]theta[/math], such as [math](3pi)/7[/math] and [math](8pi)/11[/math], the equation [math]sin(theta+2pi) = sin(theta)[/math] is valid. Therefore, it is true for all values of [math]theta[/math].
  3. For [math]T=2pi[/math], [math]theta + T[/math] and [math]theta[/math] are coterminal angles for any value of [math]theta[/math]. Therefore, referring to the unit circle, [math]sin(theta)=b[/math] and [math]sin(theta+2pi)=b[/math], and therefore [math]sin(theta+2pi)=sin(theta)[/math].
  4. There are no other values of [math]T[/math] such that [math]sin(x+T) = sin(x)[/math].
Grade 11 Trigonometry CCSS: HSF-TF.A.4
Which of the following are equal to sin(-[math](5π)/6[/math])? Choose all that apply.
  1. [math]sin((11π)/6)[/math]
  2. [math]sin((19π)/6)[/math]
  3. [math]sin((-7π)/6)[/math]
  4. [math]sin((17π)/6)[/math]
Grade 11 Trigonometry CCSS: HSF-TF.A.4
Let [math]0 ≤ θ ≤ π/2[/math] be an angle whose terminal arm intersects circle B at (x₁, y₁). What is the value of cos(θ)?
  1. [math]x_1[/math]
  2. [math]y_1[/math]
  3. [math]y_1/x_1[/math]
  4. [math]x_1/y_1[/math]
Grade 11 Trigonometry CCSS: HSF-TF.A.4
Which of the following are equal to tan([math](3π)/4[/math])? Choose all that apply.
  1. [math]tan(-(5π)/4)[/math]
  2. [math]tan((11π)/4)[/math]
  3. [math]tan(-(π)/4)[/math]
  4. [math]tan((7π)/4)[/math]
Grade 11 Trigonometry CCSS: HSF-TF.A.4
Which of the following demonstrates the periodicity of the sine function?
  1. sin(−θ) = −sin(θ)
  2. sin(θ) = cos(π/2 − θ)
  3. sin(θ + 2π) = sin(θ)
  4. sin(π − θ) = sin(θ)
Grade 11 Trigonometry CCSS: HSF-TF.A.4

This question is a part of a group with common instructions. View group »

What conclusion from the previous questions can be reached?
  1. [math]sin(theta) = y_1[/math] and [math]sin(-theta) = -x_1[/math] for [math]0 <= theta <= pi/2[/math].
  2. [math]sin(theta) = y_1/x_1 = 1/sin(-theta)[/math] for [math]0 <= theta <= pi/2[/math].
  3. [math]sin(theta) = y_1/x_1 = -sin(-theta)[/math] for [math]0 <= theta <= pi/2[/math].
  4. [math]sin(theta) = y_1 = -sin(-theta)[/math] for [math]0 <= theta <= pi/2[/math].
Grade 11 Trigonometry CCSS: HSF-TF.A.4

This question is a part of a group with common instructions. View group »

The period of the cosine function is also [math]2pi[/math], and showing this is true is similar to the process used for the sine function. However, the period of the tangent function is [math]pi[/math]. Which of the following equations correctly shows why the period of tangent is [math]pi?[/math]
  1. [math]tan(theta + pi) = sin(theta+pi)/cos(theta+pi) = (-sin(theta))/(-cos(theta)) = sin(theta)/cos(theta) = tan(theta)[/math]
  2. [math]tan(theta + pi) = sin(theta+pi)/cos(theta+pi) = (sin(theta)+pi)/(cos(theta)+pi) = sin(theta)/cos(theta) = tan(theta)[/math]
  3. [math]tan(theta + pi) = sin(theta+pi)/cos(theta+pi) = (sin(theta)+sin(pi))/(cos(theta)+cos(pi)) = (sin(theta)+0)/(cos(theta)+0) = tan(theta)[/math]
  4. [math]tan(theta + pi) = tan(theta) + tan(pi) = tan(theta)[/math]
Grade 11 Trigonometry CCSS: HSF-TF.A.4
Which of the following are equal to cos(0)? Choose all that apply.
  1. cos(2π)
  2. cos(-4π)
  3. cos(π)
  4. cos(6π)
Grade 11 Trigonometry CCSS: HSF-TF.A.4
For −θ, where would the terminal arm intersect circle B?
  1. [math](−x_1, −y_1)[/math]
  2. [math](−x_1, y_1)[/math]
  3. [math](x_1, −y_1)[/math]
  4. [math](x_1, y_1)[/math]
Grade 11 Trigonometry CCSS: HSF-TF.A.4
Let [math]0 ≤ θ ≤ π/2[/math] be an angle whose terminal side intersects circle U at point P = (x₁, y₁). What is the value of cos(θ)?
  1. [math]y_1[/math]
  2. [math]x_1[/math]
  3. [math]y_1/x_1[/math]
  4. [math]x_1/y_1[/math]
Grade 11 Trigonometry CCSS: HSF-TF.A.4

This question is a part of a group with common instructions. View group »

Let [math]pi/2 < alpha <= pi[/math] be an angle in standard position, whose terminal arm intersects circle A at [math](-x_2, y_2)[/math]. Can the same conclusion be reached concerning [math]sin(alpha)[/math] as was reached for [math]sin(theta)[/math], with the same reasoning? Why?
  1. Yes, since neither conclusion depends upon the x-values (it doesn't matter if they're positive or negative).
  2. Yes, since [math]sin(alpha) = sin(theta)[/math].
  3. No, because the reasoning applied is only valid for angles in the first quadrant.
  4. No, because the sine function is only positive in the first quadrant.
Grade 11 Trigonometry CCSS: HSF-TF.A.4
Which of the following are equal to sin([math](2π)/3[/math])? Choose all that apply.
  1. [math] sin(π/3)[/math]
  2. [math] sin(7π/3)[/math]
  3. [math] sin(-4π/3)[/math]
  4. [math] sin(5π/3)[/math]
Grade 11 Trigonometry CCSS: HSF-TF.A.4
Which of the following are equal to sin(-[math]π/4[/math])? Choose all that apply.
  1. [math]sin((7π)/4)[/math]
  2. [math]sin((9π)/4)[/math]
  3. [math]sin((3π)/4)[/math]
  4. [math]sin((-9π)/4)[/math]
Grade 11 Trigonometry CCSS: HSF-TF.A.4
Let [math]π/2 < α ≤ π[/math] be an angle whose terminal arm intersects circle B at (−x₂, y₂). Can the same conclusion be reached concerning cos(α)? Why?
  1. Yes, because the cosine of an angle is always the x-coordinate on the unit circle.
  2. No, because cosine is only positive in the first quadrant.
  3. No, because the reasoning applies only when x is positive.
  4. Yes, because cos(α) = cos(θ).
Grade 11 Trigonometry CCSS: HSF-TF.A.4
For the angle −θ, where would the terminal arm intersect circle U?
  1. [math](−x_1, −y_1)[/math]
  2. [math](−x_1, y_1)[/math]
  3. [math](x_1, −y_1)[/math]
  4. [math](x_1, y_1)[/math]
Grade 11 Trigonometry CCSS: HSF-TF.A.4
For −θ, where would the terminal arm intersect circle A?
  1. [math](−x_1, −y_1)[/math]
  2. [math](−x_1, y_1)[/math]
  3. [math](x_1, −y_1)[/math]
  4. [math](x_1, y_1)[/math]
Grade 11 Trigonometry CCSS: HSF-TF.A.4

This question is a part of a group with common instructions. View group »

Looking at [math]pi < beta <= (3pi)/2[/math] and [math](3pi)/2 < gamma <= 2pi[/math], where both angles are in standard position, and their terminal arms intersect circle A at [math](-x_3, -y_3)[/math] and [math](x_4, -y_4)[/math] respectively, which of the following explains why the sine of an angle equals the negative sine of the negative of that angle for angles between [math]pi[/math] and [math]2pi ?[/math]
  1. Since sine is periodic, whatever is true for the sine function for values between [math]0[/math] and [math]pi[/math] must also be true for values between [math]pi[/math] and [math]2pi[/math].
  2. Using the same reasoning as before, for angle [math]beta[/math] it follows that [math]sin(beta) = -y_3 = -sin(-beta)[/math] and for angle [math]gamma[/math] that [math]sin(gamma) = -y_4 = -sin(-gamma)[/math].
  3. As seen before, the sine of an angle in one quadrant is always the opposite of the sine of an angle in an adjacent quadrant. Thus [math]sin(beta) = -sin(-beta)[/math] and [math]sin(gamma) = - sin(-gamma)[/math].
  4. Looking at angles between [math]pi[/math] and [math]2pi[/math], the sine of these angles is always negative. Therefore, [math]sin(beta) = - sin(-beta)[/math] and [math]sin(gamma) = - sin(-gamma)[/math].
Grade 11 Trigonometry CCSS: HSF-TF.A.4
Which of the following is NOT true for the sine function?
  1. sin(θ + 2π) = sin(θ)
  2. sin(-θ) = sin(θ)
  3. sin(π − θ) = sin(θ)
  4. sin(θ + π) = -sin(θ)
Previous Page 1 of 5 Next

Become a Pro subscriber to access Common Core questions

Unlimited premium printables Unlimited online testing Unlimited custom tests

Learn More About Benefits and Options

You need to have at least 5 reputation to vote a question down. Learn How To Earn Badges.