AnswersPrecalculusAnalytic Trigonometry

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What is the exact value of sine of open paren 105 degrees 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 minus square root of 3 end root and denominator 2
C
the fraction with numerator square root of 2 plus square root of 3 end root and denominator 2
D
negative the fraction with numerator square root of 2 minus square root of 3 end root and denominator 2
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What is the value of 1 minus 2 sine squared open paren 105 degrees close paren ?

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

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

A
negative 2 plus square root of 3
B
1 plus square root of 3
C
1 minus square root of 3
D
negative 2 minus square root of 3
4

What is the exact value of tangent of open paren 195 degrees close paren ?

A
the fraction with numerator square root of 3 plus 1 and denominator 1 minus square root of 3
B
the fraction with numerator square root of 3 minus 3 and denominator 3 plus square root of 3
C
the fraction with numerator square root of 3 minus 1 and denominator 1 plus square root of 3
D
the fraction with numerator square root of 3 plus 3 and denominator 3 minus square root of 3
5

Which statement is true about the graph of the equation y is equal to cosecant inverse of x ?

A
There is a vertical asymptote at x is equal to 0 .
B
There is a horizontal asymptote at y is equal to 0 .
C
There is a vertical asymptote at x is equal to pi over 2 .
D
There is a horizontal asymptote at y is equal to pi over 2 .
6

Which is the graph of y is equal to arctan times x ?

A
Image with description A coordinate plane with a graph. From (0 comma 0), a curve decreases and approaches infinity as x approaches negative 1 from the right. From (0 comma 0), it increases and approaches negative infinity as x approaches 1 from the left.
B
Image with description A coordinate plane with a graph. From (0 comma negative 1), a curve increases and approaches the x-axis as x approaches negative infinity from the right. From (0 comma 1), a curve decreases and approaches the x-axis as x approaches infinity from the left.
C
Image with description A coordinate plane with a graph. From (0 comma 0), a curve decreases and approaches negative infinity as x approaches negative 1 from the right. From (0 comma 0), it increases and approaches infinity as x approaches 1 from the left.
D
Image with description A coordinate plane. The graph starts and rises to (negative 4 pi comma 1.5). It falls through (negative 3 pi comma 1) to (negative 2 pi comma 0.5). It then rises through (negative pi comma 1) to (0 comma 1.5). It then falls through (pi comma 1) to (2 pi comma 0.5). It then rises through (3 pi comma 1) to (4 pi comma 1.5).
7

The equations y is equal to tangent squared of x and y is equal to 1 are graphed here. According to the graph, which of the following is part of the solution to the trigonometric inequality tangent squared of x is less than 1 over the interval 0 is less than or equal to x comma x is less than or equal to 2 pi radians?

A
x is equal to 2 pi over 3
B
x is equal to 3 pi over 2
C
x is equal to 4 pi over 3
D
x is equal to pi over 6
8

Based on the diagram, which equation can be simplified to derive the cosine sum identity?

A
square root of open paren cosine of open paren u plus v close paren minus 1 close paren squared plus open paren sine of open paren u plus v close paren minus 0 close paren squared end root is equal to square root of open paren cosine of negative v minus 1 close paren squared plus open paren sine of negative v minus 0 close paren squared end root
B
square root of open paren cosine of open paren u plus v close paren minus 1 close paren squared plus open paren sine of open paren u plus v close paren minus 0 close paren squared end root is equal to square root of open paren cosine of u minus cosine of negative v close paren squared plus open paren sine of u minus sine of negative v close paren squared end root
C
square root of open paren cosine of open paren u plus v close paren minus 1 close paren squared plus open paren sine of open paren u plus v close paren minus 0 close paren squared end root is equal to square root of open paren cosine of open paren u plus v close paren minus cosine of u close paren squared plus open paren sine of open paren u plus v close paren minus sine of u close paren squared end root
D
square root of open paren cosine of open paren u plus v close paren minus 1 close paren squared plus open paren sine of open paren u plus v close paren minus 0 close paren squared end root is equal to square root of open paren cosine of u minus 1 close paren squared plus open paren sine of u minus 0 close paren squared end root
9

In which step did she first make an error, and what was the error?

A
She first made an error in step 5 because she did not correctly graph y is equal to cotangent of x minus cosecant of x .
B
She first made an error in step 4 because the simplified form of the inequality should have been 1 is less than or equal to cotangent of x plus cosecant of x instead of 1 is less than or equal to cotangent of x minus cosecant of x .
C
She first made an error in step 6 because she chose the wrong interval in which the graph of one equation is at or above the graph of the other equation.
D
She first made an error in step 3 because she should not have subtracted 2 cotangent x and added 3 cosecant x to the right side of the inequality.
10

Which expression will complete step 2 in the proof?

A
square root of 1 minus cosine of x end root
B
1 minus cosine of x
C
1 plus cosine of x
D
square root of 1 plus cosine of x end root
11

Which of the following complete step 4 of the proof?

A
1 and 1
B
open paren cosine squared cap A plus sine squared cap A close paren times open paren cosine squared cap b plus sine squared cap b close paren and cosine squared of open paren cap A minus cap b close paren times sine squared of open paren cap A minus cap b close paren
C
2 and 1
D
open paren cosine cap A close paren squared times open paren sine cap A close paren squared and cosine squared of open paren cap A minus cap b close paren times sine squared of open paren cap A minus cap b close paren
12

What is the missing step and reason?

A
is equal to the fraction with numerator tangent of x plus tangent of x and denominator 1 plus tangent x ; tangent sum identity
B
is equal to the fraction with numerator tangent of x plus tangent of x and denominator 1 plus tangent x ; tangent double angle identity
C
is equal to the fraction with numerator tangent of x plus tangent of x and denominator 1 minus tangent x ; tangent sum identity
D
is equal to the fraction with numerator tangent of x plus tangent of x and denominator 1 minus tangent x ; tangent double angle identity

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