Common Core Standard HSF-TF.C.9 Questions

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Grade 11 Trigonometry CCSS: HSF-TF.C.9

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What is the missing reason in step 18?

Reciprocal Identity
Radii of the same circle are equal
Transitive Property of Equality
Pythagorean Theorem

Grade 11 Trigonometry CCSS: HSF-TF.C.9

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What is the missing expression in step 5?

$( ( \ sin(alpha)cos(beta) + sin(beta)cos(alpha) \ ))/( ( \ cos(alpha)cos(beta) \ ) ( \ cos(alpha)cos(beta) - sin(alpha)sin(beta) \ ))$

$\ \$

$( ( \ cos(alpha)cos(beta) \ )( \ sin(alpha)cos(beta) + sin(beta)cos(alpha) \ ))/(( \ cos(alpha)cos(beta) - sin(alpha)sin(beta) \ ))$

$\ \$

$( ( \ cos(alpha)cos(beta) \ )( \ sin(alpha)cos(beta) + sin(beta)cos(alpha) \ ))/( ( \ cos(alpha)cos(beta) \ ) ( \ cos(alpha)cos(beta) - sin(alpha)sin(beta) \ ))$

$\ \$

$( ( \ sin(alpha)cos(beta) \ )( \ sin(beta)cos(alpha) \ ))/( ( \ cos(alpha)cos(beta) \ ) ( \ sin(alpha)sin(beta) \ ))$

$\ \$

Grade 12 Trigonometry CCSS: HSF-TF.C.9

Prove that

$cos(2theta) = cos^2(theta) - sin^2(theta)$ .

Grade 11 Trigonometry CCSS: HSF-TF.C.9

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Which of the following is equal to

$cos(-theta) ?$

$cos(theta)$
$-cos(theta)$
$-cos(-theta)$
$cos(theta-1)$

Grade 11 Trigonometry CCSS: HSF-TF.C.9

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What is the missing explanation in step 1?

$"Definition of tangent"$
$"Pythagorean Identity"$
$"Law of S""ines"$
$alpha/alpha = 1, \ beta/beta = 1$

Grade 12 Trigonometry CCSS: HSF-TF.C.9

Given that

$cos(2theta) = cos^2(theta)- sin^2(theta)$ , prove that

$cos(2theta) = 2cos^2(theta)-1$ .

Grade 11 Trigonometry CCSS: HSF-TF.C.9

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Which of the following is equal to

$sin(-theta) ?$

$sin(theta)$
$-sin(theta)$
$-sin(-theta)$
$sin(theta-1)$

Grade 11 Trigonometry CCSS: HSF-TF.C.9

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What is the missing expression in step 2?

$(((sin(alpha)cos(beta))/(cos(alpha)sin(beta))))/((1-sin(alpha)/cos(alpha) sin(beta)/cos(beta)))$ $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \$ $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \$
$(((sin(alpha)sin(beta))/(cos(alpha)cos(beta))))/((1-sin(alpha)/cos(alpha) sin(beta)/cos(beta)))$ $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \$ $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \$
$(((sin(alpha)cos(alpha) \ + \ sin(beta)cos(beta))/(cos(alpha)cos(beta))))/((1-sin(alpha)/cos(alpha) sin(beta)/cos(beta)))$ $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \$ $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \$
$(((sin(alpha)cos(beta) \ + \ sin(beta)cos(alpha))/(cos(alpha)cos(beta))))/((1-sin(alpha)/cos(alpha) sin(beta)/cos(beta)))$

Grade 12 Trigonometry CCSS: HSF-TF.C.9

Given that

$cos(2theta) = cos^2(theta)-sin^2(theta)$ , prove that

$cos(2theta) = 1-2sin^2(theta)$ .

Grade 11 Trigonometry CCSS: HSF-TF.C.9

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Given the information in the previous two questions, along with the fact that

$cos(theta - alpha) = cos(theta)cos(alpha) + sin(theta)sin(alpha)$ , prove that

$cos(theta + alpha) = cos(theta)cos(alpha) - sin(theta)sin(alpha)$ .

Grade 11 Trigonometry CCSS: HSF-TF.C.9

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What is the missing explanation in step 3?

$"The sine and cosine functions are never greater than 1"$
$cos^2(theta)+ sin^2(theta)=1$
$cos(0)=1, \ sin(90°)=1$
$"The number 1 can be rewritten as a given quantity divided by itself"$

Grade 12 Trigonometry CCSS: HSF-TF.C.9

Prove that

$tan(2theta) = (2tan(theta))/(1-tan^2(theta))$ .

Grade 11 Trigonometry CCSS: HSF-TF.C.9

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What is the missing reason in step 4?

Distributive Property of Multiplication
Commutative Property of Multiplication
SSA formula for area of a triangle
Law of Sines

Grade 11 Trigonometry CCSS: HSF-TF.C.9

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What is the missing explanation in step 6?

Pythagorean Identity
Cancel like factors
Substitution Property of Equality
Division Property of Identity

Grade 12 Trigonometry CCSS: HSF-TF.C.9

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What are some of the implicit restrictions in the above proof? Choose all correct answers.

$0 < theta+alpha < pi$ , where $theta,alpha$ must both be positive real numbers.
$0 < theta+alpha < pi/2$ , where $theta, alpha$ must both be positive real numbers.
$Delta ABC$ cannot be a right triangle.
$ang BAC$ and $angBCA$ must both be acute angles.

Grade 11 Trigonometry CCSS: HSF-TF.C.9

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What is the missing reason in step 7?

Given
Right triangles have 2 sets of perpendicular sides
Triangle Property
SSS Property of Similarity

Grade 11 Trigonometry CCSS: HSF-TF.C.9

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What is the missing explanation in step 7?

Substitute in the sine addition formula
Apply the Law of Sines
Cancel like terms
Factor out like terms

Grade 11 Trigonometry CCSS: HSF-TF.C.9

For

$theta, alpha in RR$ , prove that

$sin(theta-alpha) = sin(theta)cos(alpha) - sin(alpha)cos(theta)$ given that

$sin(theta + alpha) = sin(theta)cos(alpha) + sin(alpha)cos(theta)$ .

Grade 11 Trigonometry CCSS: HSF-TF.C.9

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What is the missing statement in step 9?

$ang ABC$ is a right angle
Point $D$ is the midpoint of $bar{AC}$
$ang ABC$ is acute
$ang ADB, \ ang BDC$ are right angles

Grade 11 Trigonometry CCSS: HSF-TF.C.9

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What is the missing explanation in step 8?

Substitute in the cosine addition formula
Apply the Law of Cosines
Cancel like terms
Factor out like terms

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Common Core Standard HSF-TF.C.9 Questions

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