AnswersCMS 2026-2027 NC Math 4 INITIAL CREDITTrigonometric Difference Identities

Trigonometric Difference Identities — Quiz Answers

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Given: sine of cap A is equal to 5 over 13 , pi over 2 is less than cap A comma cap A is less than pi and tangent of cap b is equal to negative square root of 13 , pi over 2 is less than cap b comma cap b is less than pi What is tangent of open paren cap A minus cap b close paren ?

A
the fraction with numerator negative 5 plus 12 square root of 13 and denominator 12 plus 5 square root of 13
B
the fraction with numerator 12 plus 5 square root of 13 and denominator negative 5 plus 12 square root of 13
C
the fraction with numerator 5 plus 12 square root of 13 and denominator 12 minus 5 square root of 13
D
the fraction with numerator 12 minus 5 square root of 13 and denominator 5 plus 12 square root of 13
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What is the value of cosine of open paren 15 degrees close paren ?

A
the fraction with numerator square root of 6 minus square root of 2 and denominator 4
B
the fraction with numerator square root of 6 minus square root of 2 and denominator 2
C
the fraction with numerator square root of 6 plus square root of 2 and denominator 2
D
the fraction with numerator square root of 6 plus square root of 2 and denominator 4
3

Which expression is equivalent to sine open paren 20 degrees close paren minus cosine open paren 20 degrees close paren ?

A
cosine of open paren negative 60 degrees close paren
B
sine of open paren 60 degrees close paren
C
cosine of open paren 60 degrees close paren
D
sine of open paren negative 60 degrees close paren
4

Which expression is equivalent to cosine open paren 40 degrees close paren plus sine open paren 40 degrees close paren ?

A
cosine of open paren 40 degrees minus 10 degrees close paren
B
cosine of open paren 40 degrees plus 10 degrees close paren
C
sine of open paren 40 degrees minus 10 degrees close paren
D
sine of open paren 40 degrees plus 10 degrees close paren
5

What is the exact value of tangent of open paren 19 pi over 12 close paren ?

A
the fraction with numerator 3 plus square root of 3 and denominator 3 minus square root of 3
B
the fraction with numerator 1 minus square root of 3 and denominator 1 plus square root of 3
C
the fraction with numerator 3 minus square root of 3 and denominator 3 plus square root of 3
D
the fraction with numerator 1 plus square root of 3 and denominator 1 minus square root of 3
6

Which expression is equivalent to sine open paren pi over 12 close paren minus cosine open paren pi over 12 close paren ?

A
cosine of open paren negative pi over 2 close paren
B
sine of open paren negative pi over 2 close paren
C
cosine of open paren 2 pi over 3 close paren
D
sine of open paren 2 pi over 3 close paren
7

What is the exact value of sine of open paren 7 pi over 12 close paren ?

A
the fraction with numerator square root of 6 plus square root of 2 and denominator 4
B
the fraction with numerator square root of 6 minus square root of 2 and denominator 4
C
the fraction with numerator square root of 6 minus square root of 2 and denominator 8
D
the fraction with numerator square root of 6 plus square root of 2 and denominator 8
8

Which values are two of the possible solutions to the equation? sine of open paren 5 x minus pi close paren is equal to the fraction with numerator square root of 2 and denominator 2 , 0 is less than or equal to x comma x is less than 2 pi

A
start set 5 pi over 4 comma 7 pi over 4 end set
B
start set pi over 20 comma 3 pi over 20 end set
C
start set pi over 4 comma 7 pi over 4 end set
D
start set pi over 4 comma 7 pi over 20 end set
9

When simplified, the fraction with numerator tangent of open paren 40 degrees close paren minus tangent of open paren 10 degrees close paren and denominator 1 plus tangent of open paren 40 degrees close paren times tangent of open paren 10 degrees close paren is equivalent to which expression?

A
tangent of open paren negative 50 degrees close paren
B
tangent of open paren negative 30 degrees close paren
C
tangent of open paren 30 degrees close paren
D
tangent of open paren 50 degrees close paren
10

What is the value of sine open paren 80 degrees close paren minus cosine open paren 80 degrees close paren ?

A
1 half
B
negative the fraction with numerator square root of 3 and denominator 2
C
the fraction with numerator square root of 3 and denominator 2
D
negative 1 half

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