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# Common Core Standard HSF-TF.C.9 Questions

(+) Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

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What is the missing reason in step 7?
1. Substitution Property of Equality
3. Identity Property
4. Pythagorean Theorem
What is the exact value of $cos(105°) ?$
1. $(sqrt(2)-sqrt(6))/4$
2. $-(sqrt(2)+sqrt(6))/4$
3. $-1/2 + sqrt(6)/4$
4. $(sqrt(6)-sqrt(2))/4$
What is the exact value of $sin(345°) ?$
1. $1/2(sqrt(2)-1)$
2. $-1/4 (sqrt(2)+sqrt(6))$
3. $1/4(sqrt(6) - sqrt(2))$
4. $1/4(sqrt(2) - sqrt(6))$

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What is the missing reason in step 10?
1. Trigonometric Identity
2. Length of a line segment
3. Pythagorean Identity
4. Law of Sines
What is the exact value of $tan(75°) ?$
1. $-2+sqrt(3)$
2. $2+sqrt(3)$
3. $1$
4. $2-sqrt(3)$
What is the exact value of $tan(165°) ?$
1. $2-sqrt(3)$
2. $-2-sqrt(3)$
3. $2+sqrt(3)$
4. $-2+sqrt(3)$

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What is the missing statement in step 13?
1. $AB^2 = cos^2(alpha)sin^2(alpha) + cos^2(theta) sin^2(theta) - 2cos(alpha)sin(alpha)cos(theta)sin(theta)$
2. $AB^2 = cos^2(alpha) - 2cos(alpha)sin(alpha) + sin^2(alpha) + cos^2(theta) - 2cos(theta)sin(theta) + sin^2(theta)$
3. $AB^2 = cos^2(alpha) - 2cos(alpha)cos(theta) + cos^2(theta) + sin^2(alpha) - 2sin(alpha)sin(theta) + sin^2(theta)$
4. $AB^2 = cos^2(alpha) + cos^2(theta) + sin^2(alpha) + sin^2(theta)$
What is the value of $cos(165°) ?$
1. $1/4(sqrt(2)-sqrt(6))$
2. $-1/4(sqrt(2)+sqrt(6))$
3. $1/4(-sqrt(2)+sqrt(6))$
4. $1/2(-sqrt(2)+sqrt(3))$
What is the exact value of $sin(105°) ?$
1. $1/2(sqrt(3)+sqrt(2))$
2. $1/4(sqrt(2)-sqrt(6))$
3. $1/4(sqrt(6)+sqrt(2))$
4. $1/4(sqrt(6)-sqrt(2))$

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What is the missing reason in step 15?
2. Pythagorean Identity
3. Substitution Property of Equality
4. Given
What is the exact value of $sin(195°) ?$
1. $-1/2(sqrt(2)+sqrt(3))$
2. $-1/4(sqrt(6) + sqrt(2))$
3. $1/4(sqrt(2) - sqrt(6))$
4. $1/4(sqrt(6) - sqrt(2))$

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What is the missing reason in step 18?
1. Reciprocal Identity
2. Radii of the same circle are equal
3. Transitive Property of Equality
4. Pythagorean Theorem

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What is the missing expression in step 5?
1.  $( ( \ sin(alpha)cos(beta) + sin(beta)cos(alpha) \ ))/( ( \ cos(alpha)cos(beta) \ ) ( \ cos(alpha)cos(beta) - sin(alpha)sin(beta) \ ))$ $\ \$
2.  $( ( \ cos(alpha)cos(beta) \ )( \ sin(alpha)cos(beta) + sin(beta)cos(alpha) \ ))/(( \ cos(alpha)cos(beta) - sin(alpha)sin(beta) \ ))$ $\ \$
3.  $( ( \ cos(alpha)cos(beta) \ )( \ sin(alpha)cos(beta) + sin(beta)cos(alpha) \ ))/( ( \ cos(alpha)cos(beta) \ ) ( \ cos(alpha)cos(beta) - sin(alpha)sin(beta) \ ))$ $\ \$
4.  $( ( \ sin(alpha)cos(beta) \ )( \ sin(beta)cos(alpha) \ ))/( ( \ cos(alpha)cos(beta) \ ) ( \ sin(alpha)sin(beta) \ ))$ $\ \$

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Which of the following is equal to $cos(-theta) ?$
1. $cos(theta)$
2. $-cos(theta)$
3. $-cos(-theta)$
4. $cos(theta-1)$

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What is the missing explanation in step 1?
1. $"Definition of tangent"$
2. $"Pythagorean Identity"$
3. $"Law of S""ines"$
4. $alpha/alpha = 1, \ beta/beta = 1$

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Which of the following is equal to $sin(-theta) ?$
1. $sin(theta)$
2. $-sin(theta)$
3. $-sin(-theta)$
4. $sin(theta-1)$
1. $(((sin(alpha)cos(beta))/(cos(alpha)sin(beta))))/((1-sin(alpha)/cos(alpha) sin(beta)/cos(beta)))$ $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \$ $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \$
2. $(((sin(alpha)sin(beta))/(cos(alpha)cos(beta))))/((1-sin(alpha)/cos(alpha) sin(beta)/cos(beta)))$ $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \$ $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \$
3. $(((sin(alpha)cos(alpha) \ + \ sin(beta)cos(beta))/(cos(alpha)cos(beta))))/((1-sin(alpha)/cos(alpha) sin(beta)/cos(beta)))$ $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \$ $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \$
4. $(((sin(alpha)cos(beta) \ + \ sin(beta)cos(alpha))/(cos(alpha)cos(beta))))/((1-sin(alpha)/cos(alpha) sin(beta)/cos(beta)))$