AnswersPrecalculusTrigonometric Double Angle Identities

Trigonometric Double Angle Identities — Quiz Answers

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Which expression is equivalent to the fraction with numerator 1 and denominator 1 minus 2 sine squared x ?

A
1 over cosine of 2 x
B
sine of 2 x
C
1 over sine of 2 x
D
cosine of 2 x
2
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Suppose sine of x is equal to 4 fifths and cosine of x is less than 0 What is the value of cosine of 2 x ?

A
7 over 25
B
14 over 25
C
negative 14 over 25
D
negative 7 over 25
3

Suppose cosine of x is equal to negative 1 third , where pi over 2 is less than or equal to x comma x is less than or equal to pi What is the value of tangent of 2 x ?

A
negative square root of 8
B
the fraction with numerator 2 square root of 8 and denominator 7
C
square root of 8
D
negative the fraction with numerator 2 square root of 8 and denominator 7
4

Which expression is equivalent to cosine of 4 x ?

A
2 cosine squared x minus 4
B
4 cosine squared x
C
2 cosine squared x minus 1
D
2 times open paren 2 cosine squared x minus 1 close paren squared minus 1
5

What is the value of 2 cosine squared open paren 75 degrees close paren minus 1 ?

A
1 half
B
negative 1 half
C
the fraction with numerator square root of 3 and denominator 2
D
negative the fraction with numerator square root of 3 and denominator 2
6

Which expression is equal to 2 sine open paren pi over 10 close paren cosine open paren pi over 10 close paren ?

A
sine pi over 5
B
negative sine times open paren pi over 5 close paren
C
negative sine times open paren pi over 20 close paren
D
sine pi over 20
7

Which derivation correctly uses the cosine sum identity to prove the cosine double angle identity?

A
Table with 2 columns and 4 rows.Row 1: Column 1, empty; Column 2, 'Step' Row 2: Column 1, '1.'; Column 2, 'cosine of 2 x is equal to cosine of open paren x plus x close paren' Row 3: Column 1, '2.'; Column 2, 'is equal to sine x plus cosine x' Row 4: Column 1, '3.'; Column 2, 'is equal to sine squared of x plus cosine squared of x'
B
Table with 2 columns and 4 rows.Row 1: Column 1, empty; Column 2, 'Step' Row 2: Column 1, '1.'; Column 2, 'cosine of 2 x is equal to cosine of open paren x plus x close paren' Row 3: Column 1, '2.'; Column 2, 'is equal to cosine x plus sine x' Row 4: Column 1, '3.'; Column 2, 'is equal to cosine squared of x plus sine squared of x'
C
Table with 2 columns and 4 rows.Row 1: Column 1, empty; Column 2, 'Step' Row 2: Column 1, '1.'; Column 2, 'cosine of 2 x is equal to cosine of open paren x plus x close paren' Row 3: Column 1, '2.'; Column 2, 'is equal to cosine x minus sine x' Row 4: Column 1, '3.'; Column 2, 'is equal to cosine squared of x minus sine squared of x'
D
Table with 2 columns and 4 rows.Row 1: Column 1, empty; Column 2, 'Step' Row 2: Column 1, '1.'; Column 2, 'cosine of 2 x is equal to cosine of open paren x plus x close paren' Row 3: Column 1, '2.'; Column 2, 'is equal to sine x minus cosine x' Row 4: Column 1, '3.'; Column 2, 'is equal to sine squared of x minus cosine squared of x'
8

Simplify the fraction with numerator cosine of 2 x and denominator cosine of x minus sine of x

A
cosine of x minus sine of x
B
the fraction with numerator 2 sine x cosine x and denominator sine of x minus cosine of x
C
the fraction with numerator 2 sine x cosine x and denominator cosine of x minus sine of x
D
cosine of x plus sine of x
9

If tangent of x is equal to 3 fifths and sine of x is greater than 0 , what is sine of 2 x ?

A
the fraction with numerator 3 and denominator square root of 34
B
the fraction with numerator 6 and denominator square root of 34
C
30 over 34
D
9 over 34
10

Suppose tangent of x is equal to 7 halves where 180°<x<270° What is the value of sine of 2 x ?

A
28 over 53
B
the fraction with numerator 14 and denominator square root of 53
C
the fraction with numerator 7 and denominator square root of 53
D
49 over 53

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