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Flashcards: Unit Circle in the Coordinate Plane: CCSS.Math.Content.HSF-TF.A.2

$\theta$ $\displaystyle \theta$ is the angle between the $\displaystyle x$ -axis and the line that connects the origin to the point (5,12) $\displaystyle (5,12)$ .

Calculate $\sin(\theta)$ $\displaystyle \sin(\theta)$ .

$\sin(\theta)=\frac{5}{12}$ $\displaystyle \sin(\theta)=\frac{5}{12}$

$\sin(\theta)=12$ $\displaystyle \sin(\theta)=12$

$\sin(\theta)=5$ $\displaystyle \sin(\theta)=5$

$\sin(\theta)=\frac{12}{5}$ $\displaystyle \sin(\theta)=\frac{12}{5}$

$\sin(\theta)=13$ $\displaystyle \sin(\theta)=13$

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All Common Core: High School - Functions Resources

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Flashcards: Unit Circle in the Coordinate Plane: CCSS.Math.Content.HSF-TF.A.2

$\theta$ $\displaystyle \theta$ is the angle between the $\displaystyle x$ -axis and the line that connects the origin to the point (5,12) $\displaystyle (5,12)$ .

Calculate $\sin(\theta)$ $\displaystyle \sin(\theta)$ .

$\sin(\theta)=\frac{5}{12}$ $\displaystyle \sin(\theta)=\frac{5}{12}$

$\sin(\theta)=12$ $\displaystyle \sin(\theta)=12$

$\sin(\theta)=5$ $\displaystyle \sin(\theta)=5$

$\sin(\theta)=\frac{12}{5}$ $\displaystyle \sin(\theta)=\frac{12}{5}$

$\sin(\theta)=13$ $\displaystyle \sin(\theta)=13$

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Flashcards: Unit Circle in the Coordinate Plane: CCSS.Math.Content.HSF-TF.A.2

$\theta$ $\displaystyle \theta$ is the angle between the $\displaystyle x$ -axis and the line that connects the origin to the point (5,12) $\displaystyle (5,12)$ .

Calculate $\sin(\theta)$ $\displaystyle \sin(\theta)$ .

Your answer:

$\sin(\theta)=\frac{5}{12}$ $\displaystyle \sin(\theta)=\frac{5}{12}$

Your answer:

$\sin(\theta)=5$ $\displaystyle \sin(\theta)=5$

Your answer:

$\sin(\theta)=\frac{12}{5}$ $\displaystyle \sin(\theta)=\frac{12}{5}$

Your answer:

$\sin(\theta)=13$ $\displaystyle \sin(\theta)=13$

Correct answer:

$\sin(\theta)=12$ $\displaystyle \sin(\theta)=12$

Explanation:

This question is testing one's ability to understand the trigonometric relationships and how the relate to the unit circle for solving problems.

For the purpose of Common Core Standards, "Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle." falls within the Cluster A of "Extend the domain of trigonometric functions using the unit circle" concept (CCSS.MATH.CONTENT.HSF-TF.A.2).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Plot the line that connects the origin to the point (5,12) $\displaystyle (5,12)$ .

Screen shot 2016 01 14 at 11.03.26 am

Step 2: Use right triangles and the unit circle to identify the trigonometric characteristics of the describe situation.

The unit circle is an extremely helpful tool in solving trigonometric problems. For the purpose of trigonometry, the unit circle is located at the origin and has a radius of one unit. This is because right triangles can be formed using the x axis as one leg of the triangle and the line from the origin to a point on the circle as the hypotenuse with a measurement of one.

Therefore, the point on the circle has coordinates of $(\cos(x),\sin(x))$ $\displaystyle (\cos(x),\sin(x))$ for the angle that is created by the x axis and the hypotenuse. It is important to know that

$(x,y)=(\cos(\theta),\sin(\theta))$ $\displaystyle (x,y)=(\cos(\theta),\sin(\theta))$ and can be found using the triangle that is created on the unit circle.

For this particular question,

$\\(5,12)=(\cos(\theta),\sin(\theta)) \\\cos(\theta)=5 \\\sin(\theta)=12$ $\displaystyle \\(5,12)=(\cos(\theta),\sin(\theta)) \\\cos(\theta)=5 \\\sin(\theta)=12$

Step 3: Answer the question.

$\sin(\theta)=12$ $\displaystyle \sin(\theta)=12$

Flashcards: Unit Circle in the Coordinate Plane: CCSS.Math.Content.HSF-TF.A.2

$\theta$ $\displaystyle \theta$ is the angle between the $\displaystyle x$ -axis and the line that connects the origin to the point (5,12) $\displaystyle (5,12)$ .

Calculate $\cos(\theta)$ $\displaystyle \cos(\theta)$ .

$\cos(\theta)=5$ $\displaystyle \cos(\theta)=5$

$\cos(\theta)=13$ $\displaystyle \cos(\theta)=13$

$\cos(\theta)=-12$ $\displaystyle \cos(\theta)=-12$

$\cos(\theta)=-5$ $\displaystyle \cos(\theta)=-5$

$\cos(\theta)=12$ $\displaystyle \cos(\theta)=12$

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Flashcards: Unit Circle in the Coordinate Plane: CCSS.Math.Content.HSF-TF.A.2

$\theta$ $\displaystyle \theta$ is the angle between the $\displaystyle x$ -axis and the line that connects the origin to the point (5,12) $\displaystyle (5,12)$ .

Calculate $\cos(\theta)$ $\displaystyle \cos(\theta)$ .

Your answer:

$\cos(\theta)=13$ $\displaystyle \cos(\theta)=13$

Your answer:

$\cos(\theta)=-12$ $\displaystyle \cos(\theta)=-12$

Your answer:

$\cos(\theta)=-5$ $\displaystyle \cos(\theta)=-5$

Your answer:

$\cos(\theta)=12$ $\displaystyle \cos(\theta)=12$

Correct answer:

$\cos(\theta)=5$ $\displaystyle \cos(\theta)=5$

Explanation:

This question is testing one's ability to understand the trigonometric relationships and how the relate to the unit circle for solving problems.

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Plot the line that connects the origin to the point (5,12) $\displaystyle (5,12)$ .

Screen shot 2016 01 14 at 11.03.26 am

Step 2: Use right triangles and the unit circle to identify the trigonometric characteristics of the describe situation.

$(x,y)=(\cos(\theta),\sin(\theta))$ $\displaystyle (x,y)=(\cos(\theta),\sin(\theta))$ and can be found using the triangle that is created on the unit circle.

For this particular question,

$\\(5,12)=(\cos(\theta),\sin(\theta)) \\\cos(\theta)=5 \\\sin(\theta)=12$ $\displaystyle \\(5,12)=(\cos(\theta),\sin(\theta)) \\\cos(\theta)=5 \\\sin(\theta)=12$

Step 3: Answer the question.

$\cos(\theta)=5$ $\displaystyle \cos(\theta)=5$

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Flashcards: Unit Circle in the Coordinate Plane: CCSS.Math.Content.HSF-TF.A.2

All Common Core: High School - Functions Resources

Flashcards: Unit Circle in the Coordinate Plane: CCSS.Math.Content.HSF-TF.A.2

Flashcards: Unit Circle in the Coordinate Plane: CCSS.Math.Content.HSF-TF.A.2

Flashcards: Unit Circle in the Coordinate Plane: CCSS.Math.Content.HSF-TF.A.2

Flashcards: Unit Circle in the Coordinate Plane: CCSS.Math.Content.HSF-TF.A.2

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