AnswersPrecalculusTrigonometric Half Angle Identities

Trigonometric Half Angle Identities — Quiz Answers

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Which expression is equivalent to tangent of open paren theta over 2 close paren times open paren negative sine theta close paren ?

A
1 minus cosine of theta
B
negative 1 plus cosine of theta
C
negative 1 minus cosine of theta
D
1 plus cosine of theta
2
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What is the exact value of tangent of open paren 67.5 degrees close paren ?

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

What is the exact value of sine of open paren 112.5 degrees close paren ?

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

Which expression is equivalent to 4 sine squared x minus 8 sine squared open paren x over 2 close paren ?

A
4 times open paren 2 minus cosine of x minus cosine squared of x close paren
B
4 times open paren 2 plus cosine of x minus cosine squared of x close paren
C
4 times open paren cosine of x minus cosine squared of x close paren
D
4 times open paren negative cosine times x minus cosine squared of x close paren
5

For 0 is less than or equal to theta comma theta is less than 2 pi , how many solutions are there to tangent of open paren theta over 2 close paren is equal to sine of theta ? Note: Do not include values that are undefined for tangent or sine of theta

A
1
B
2
C
0
D
3
6

Which expression is equivalent to square root of the fraction with numerator 1 minus cosine of 10 x and denominator 2 end root ?

A
sine of 20 x
B
sine of 5 x
C
cosine of 20 x
D
cosine of 5 x
7

Which expression is equivalent to 2 cosine squared open paren x over 2 close paren minus mathrm cosine x ?

A
1 minus 2 cosine x
B
1
C
1 plus 2 cosine x
D
0
8

What is the exact value of sine of open paren 75 degrees close paren ?

A
the fraction with numerator square root of 2 plus square root of 3 end root and denominator 2
B
the fraction with numerator square root of 2 minus square root of 3 end root and denominator 2
C
1 half
D
the fraction with numerator square root of 3 and denominator 2
9

What is the exact value of cosine of open paren 11 pi over 12 close paren ?

A
negative the fraction with numerator square root of 2 plus square root of 3 end root and denominator 2
B
the fraction with numerator square root of 2 plus square root of 3 end root and denominator 2
C
negative the fraction with numerator square root of 2 minus square root of 3 end root and denominator 2
D
the fraction with numerator square root of 2 minus square root of 3 end root and denominator 2
10

What is the exact value of tangent of open paren 5 pi over 8 close paren ?

A
square root of the fraction with numerator 2 minus square root of 2 and denominator 2 plus square root of 2 end root
B
square root of the fraction with numerator 2 plus square root of 2 and denominator 2 minus square root of 2 end root
C
negative square root of the fraction with numerator 2 minus square root of 2 and denominator 2 plus square root of 2 end root
D
negative square root of the fraction with numerator 2 plus square root of 2 and denominator 2 minus square root of 2 end root

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