AnswersPrecalculusApplying Trigonometric Identities and Equations

Applying Trigonometric Identities and Equations — Test Answers

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Which expression is equivalent to tangent of open paren x minus pi close paren ?

A
the fraction with numerator tangent of x minus tangent of pi and denominator 1 minus tangent of x times tangent of pi
B
the fraction with numerator tangent of x plus tangent of pi and denominator 1 plus tangent of x times tangent of pi
C
the fraction with numerator tangent of x plus tangent of pi and denominator 1 minus tangent of x times tangent of pi
D
the fraction with numerator tangent of x minus tangent of pi and denominator 1 plus tangent of x times tangent of pi
2
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What is the exact value of tangent of open paren pi over 12 close paren ?

A
the fraction with numerator 3 and denominator square root of 3
B
the fraction with numerator 1 and denominator square root of 3
C
the fraction with numerator 1 and denominator 2 minus square root of 3
D
the fraction with numerator 1 and denominator 2 plus square root of 3
5

What are the possible remaining angle measures in triangle ABC with m angle cap A is equal to 40 degrees , AC is equal to 60 , and BC is equal to 45 ?

A
m angle cap b almost equal to 59 degrees , m angle cap c almost equal to 81 degrees
B
m angle cap b almost equal to 121 degrees , m angle cap c almost equal to 19 degrees and m angle cap b almost equal to 59 degrees , m angle cap c almost equal to 81 degrees
C
No triangle can be formed with these measures.
D
m angle cap b almost equal to 121 degrees , m angle cap c almost equal to 19 degrees
6

Which expression is equivalent to open paren 1 plus cosine of x close paren squared times tangent of open paren x over 2 close paren ?

A
1 minus cosine of x
B
sine of x
C
open paren 1 plus cosine of x close paren times sine of x
D
1 minus cosine squared of x
8

Which shows all the exact solutions of 2 secant squared x minus 4th power of tangent x is equal to negative 1 ? Give your answer in radians.

A
pi over 3 plus 2 k pi and 5 pi over 3 plus 2 k pi
B
pi over 3 plus k pi , 2 pi over 3 plus k pi , 4 pi over 3 plus k pi , and 5 pi over 3 plus k pi
C
pi over 3 plus k pi and 2 pi over 3 plus k pi
D
pi over 4 plus 2 k pi , 3 pi over 4 plus 2 k pi , 5 pi over 4 plus 2 k pi , and 7 pi over 4 plus 2 k pi
10

Given: tangent cap A is equal to negative square root of 15 What is the value of tangent of open paren cap A minus pi over 4 close paren ?

A
the fraction with numerator negative square root of 15 minus 1 and denominator 1 minus square root of 15
B
the fraction with numerator negative square root of 15 plus 1 and denominator 1 plus square root of 15
C
the fraction with numerator square root of 15 plus 1 and denominator 1 minus square root of 15
D
the fraction with numerator square root of 15 minus 1 and denominator 1 plus square root of 15
11

What is the fraction with numerator 2 tangent open paren 10 degrees close paren and denominator 1 minus tangent squared of open paren 10 degrees close paren expressed as a single trigonometric ratio?

A
negative tangent times open paren 20 degrees close paren
B
negative tangent times open paren 5 degrees close paren
C
tangent of open paren 20 degrees close paren
D
tangent of open paren 5 degrees close paren
12

Which expression is equivalent to cosine open paren 103 degrees close paren minus sine open paren 103 degrees close paren ?

A
sine of open paren 157 degrees close paren
B
sine of open paren 49 degrees close paren
C
cosine of open paren 49 degrees close paren
D
cosine of open paren 157 degrees close paren
13

What is the range of y is equal to secant inverse of x ?

A
left bracket negative pi over 2 comma 0 right parenthesis and left bracket 0 comma pi over 2 right bracket
B
left bracket negative pi over 2 comma 0 right parenthesis and left parenthesis 0 comma pi over 2 right bracket
C
left bracket 0 comma pi over 2 right bracket and left bracket pi over 2 comma pi right bracket
D
left bracket 0 comma pi over 2 right parenthesis and left parenthesis pi over 2 comma pi right bracket
15

What is the correct order of the steps used to derive the identity?

A
3, 4, 5, 1, 2
B
3, 4, 1, 5, 2
C
4, 5, 3, 1, 2
D
4, 3, 5, 1, 2
16

What is the area of triangle DFG ? Round to the nearest whole square unit.

A
728 square units
B
38 square units
C
364 square units
D
27 square units
17

What is the area of triangle PQR ? Round to the nearest tenth of a square unit.

A
70 point 5 square units
B
222 point 5 square units
C
185 point 4 square units
D
111 point 3 square units
18

Which equation represents a true sine ratio in triangle ABC ?

A
sine cap c is equal to A over h
B
sine cap A is equal to h over c
C
sine cap A is equal to b over c
D
sine cap c is equal to b over A
19

A child designs a flag in the shape of a rhombus, as shown in the diagram. Which expression can be used to determine the side length of the rhombus?

A
40 cosine 30 degrees
B
square root of 400 minus 40 cosine 30 degrees end root
C
the fraction with numerator 10 and denominator cosine 30 degrees
D
square root of 800 minus 800 cosine 30 degrees end root

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