Answers PrecalculusApplying Trigonometric Identities and Equations

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Which equation could be used to solve for the measure of side q in triangle QRS shown, given s is equal to 15 , cap s is equal to 45 degrees , and cap q is equal to 105 degrees ?

the fraction with numerator sine 105 degrees and denominator 15 is equal to the fraction with numerator sine 30 degrees and denominator q

the fraction with numerator sine 105 degrees and denominator q is equal to the fraction with numerator sine 30 degrees and denominator 15

the fraction with numerator 15 and denominator sine 105 degrees is equal to the fraction with numerator q and denominator sine 45 degrees

the fraction with numerator q and denominator sine 105 degrees is equal to the fraction with numerator 15 and denominator sine 45 degrees

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Which pair of equations given is a result of constructing the altitude, h , in triangle ABC ?

sine cap A is equal to b over c sine cap c is equal to b over A

sine cap c is equal to h over A sine cap b is equal to b over A

sine cap A is equal to h over c sine cap b is equal to b over c

sine cap A is equal to h over c sine cap c is equal to h over A

Based on the sketch, how far is Joey’s house from the park?

0 point 8 6 mi.

0 point 7 4 mi.

2 point 3 5 mi.

2 point 2 1 mi.

The average daily temperature, t , in degrees Fahrenheit for a city as a function of the month of the year, m , can be modeled by the equation graphed, where m is equal to 0 represents January 1 , m is equal to 1 represents February 1, m is equal to 2 represents March 1 , and so on. If the equation is t is equal to A cosine open paren pi over 6 times open paren m plus 1 close paren close paren plus k , what are the values of A and k ?

A is equal to negative 60 ; k is equal to 20

A is equal to negative 20 ; k is equal to 60

A is equal to negative 30 ; k is equal to 50

A is equal to negative 50 ; k is equal to 30

Heron’s formula: Area is equal to square root of s open paren s minus A close paren open paren s minus b close paren open paren s minus c close paren end root

15 square units

33 square units

618 square units

8 square units

Which expression will complete step 2 in the proof?

1 plus cosine of x

1 minus cosine of x

square root of 1 minus cosine of x end root

square root of 1 plus cosine of x end root

Which of the following complete step 4 of the proof?

1 and 1

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

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

2 and 1

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

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

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

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

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

What is the missing step and reason?

is equal to the fraction with numerator tangent of x plus tangent of x and denominator 1 plus tangent x ; tangent double angle identity

is equal to the fraction with numerator tangent of x plus tangent of x and denominator 1 plus tangent x ; tangent sum identity

is equal to the fraction with numerator tangent of x plus tangent of x and denominator 1 minus tangent x ; tangent double angle identity

is equal to the fraction with numerator tangent of x plus tangent of x and denominator 1 minus tangent x ; tangent sum identity

Jake and Maddie each take the closest path from their homes to the store. Based on the picture, what is the approximate difference in the distance each person traveled to the store?

6 point 4 m

5 point 9 m

1 point 4 m

7 point 7 m

A tree is growing on a hill. In an attempt to make the tree grow straight up, a 12 -foot-long wire is attached to a tree at a point 6 feet off the ground. The wire is anchored to the ground 10 feet from the base of the tree. At what angle is the tree growing in relation to the hill?

93.8 degrees

88.1 degrees

82.3 degrees

128.0 degrees

The depth of the water at the end of a pier changes periodically along with the movement of tides. On a particular day, low tides occur at 12:00 a.m. and 3:30 p.m., with a depth of 3 point 2 5 meters, while high tides occur at 7:45 a.m. and 11:15 p.m., with a depth of 8 point 7 5 meters. Which of the following equations models d , the depth of the water in meters, as a function of time, t , in hours? Let t is equal to 0 be 12:00 a.m.

d is equal to negative 2 point 7 5 cosine open paren 4 pi over 29 t close paren plus 6

d is equal to negative 3 point 7 5 cosine open paren 4 pi over 29 t close paren plus 5

d is equal to negative 2 point 7 5 cosine open paren 4 pi over 31 t close paren plus 6

d is equal to negative 3 point 7 5 cosine open paren 4 pi over 31 t close paren plus 5

What is the value of 1 minus 2 sine squared open paren 105 degrees close paren ?

1 half

negative the fraction with numerator square root of 3 and denominator 2

the fraction with numerator square root of 3 and denominator 2

negative 1 half

What is the exact value of sine of open paren 105 degrees close paren ?

the fraction with numerator square root of 2 minus square root of 3 end root and denominator 2

negative the fraction with numerator square root of 2 plus square root of 3 end root and denominator 2

the fraction with numerator square root of 2 plus square root of 3 end root and denominator 2

negative the fraction with numerator square root of 2 minus square root of 3 end root and denominator 2

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

negative 2 minus square root of 3

1 plus square root of 3

1 minus square root of 3

negative 2 plus square root of 3

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

the fraction with numerator square root of 3 minus 3 and denominator 3 plus square root of 3

the fraction with numerator square root of 3 minus 1 and denominator 1 plus square root of 3

the fraction with numerator square root of 3 plus 1 and denominator 1 minus square root of 3

the fraction with numerator square root of 3 plus 3 and denominator 3 minus square root of 3

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

There is a vertical asymptote at x is equal to pi over 2 .

There is a horizontal asymptote at y is equal to 0 .

There is a vertical asymptote at x is equal to 0 .

There is a horizontal asymptote at y is equal to pi over 2 .

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

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.

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.

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.

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).

What is one possible solution for the triangle?

YZ almost equal to 43 point 0 , m angle cap x almost equal to 94.6 degrees , m angle cap z almost equal to 17.4 degrees

YZ almost equal to 19 point 3 , m angle cap x almost equal to 26.6 degrees , m angle cap z almost equal to 85.4 degrees

YZ almost equal to 19 point 3 , m angle cap x almost equal to 85.4 degrees , m angle cap z almost equal to 26.6 degrees

YZ almost equal to 12 point 9 , m angle cap x almost equal to 17.4 degrees , m angle cap z almost equal to 85.4 degrees

What is the area of triangle DEF ?

2 square root of 14 square units

12 square root of 77 square units

6 square root of 22 square units

2 square root of 2 square units

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