27.1 Trigonometric Ratios Problem Set
TRIGONOMETRIC RATIOS | PRACTICE PROBLEMS Complete the following to reinforce your understanding of the concept covered in this module.
PROBLEM 1: Given the triangle illustrated below, the trigonometric ratio for sine is best represented as:
A. sin 𝜃 =
&
B. sin 𝜃 =
(
C. sin 𝜃 =
)
D. sin 𝜃 =
' ' * ) '
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PROBLEM 2: '
If cos 𝜃 = , the tangent can be best represented as: &
A. tan 𝜃 = B. tan 𝜃 =
( ' ) '
C. tan 𝜃 =
&
D. tan 𝜃 =
&
' '
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PROBLEM 3: )
Given that sin 𝜃 = and cos 𝜃 = '
A. 𝑠𝑒𝑐 𝜃 =
&
B. 𝑠𝑒𝑐 𝜃 =
)
C. 𝑠𝑒𝑐 𝜃 =
(
D. 𝑠𝑒𝑐 𝜃 =
'
* '
, the sec 𝜃 is best represented as:
* * * *
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PROBLEM 4:
If sin 𝑎 = 1 − 𝑥 ) , then csc 𝑎 is most close to:
A. B. C. D.
1 − 𝑥) 9 :;9 < : :;9 < 9 :=9
?
B.
A?
C.
>A
D.
>?
@ > ? A
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PROBLEM 6: For natural functions with angles between 90° and 180°, which of the following statements is true: A. The tangent is positive B. The cotangent is positive C. The cosine is negative D. The sine is negative
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PROBLEM 7: The inverse of the natural cosecant function is best represented as: A. Secant B. Sine C. Cosine D. Tangent
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PROBLEM 8: Given the defined triangle, the trigonometric ratio for cotangent is best represented as:
A. cot 𝜃 = B. cot 𝜃 = C. cot 𝜃 = D. cot 𝜃 =
* ' ( ) M ) * )
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PROBLEM 9: '
If cos 𝜃 = , the ratio for cosecant is most close to: &
A. csc 𝜃 = B. csc 𝜃 =
& ( & '
C. csc 𝜃 =
&
D. csc 𝜃 =
&
) *
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PROBLEM 10: )
Given that sin 𝜃 = and cos 𝜃 = '
A. cot 𝜃 = B. cot 𝜃 = C. cot 𝜃 = D. cot 𝜃 =
* '
, the cot 𝜃 is best represented as:
* ' ' ) * ' * )
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PROBLEM 11: If sin 𝑎 = 𝑥, then sec 𝑎 is most close to:
A. B. C. D.
1 − 𝑥) 9 :;9 < : :;9 < 9 :=9
PROBLEM 1: Given the triangle illustrated below, the trigonometric ratio for sine is best represented as:
A. sin 𝜃 =
&
B. sin 𝜃 =
(
C. sin 𝜃 =
)
D. sin 𝜃 =
' ' * ) '
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by Prepineer | Prepineer.com
PROBLEM 2: '
If cos 𝜃 = , the tangent can be best represented as: &
A. tan 𝜃 = B. tan 𝜃 =
( ' ) '
C. tan 𝜃 =
&
D. tan 𝜃 =
&
' '
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PROBLEM 3: )
Given that sin 𝜃 = and cos 𝜃 = '
A. 𝑠𝑒𝑐 𝜃 =
&
B. 𝑠𝑒𝑐 𝜃 =
)
C. 𝑠𝑒𝑐 𝜃 =
(
D. 𝑠𝑒𝑐 𝜃 =
'
* '
, the sec 𝜃 is best represented as:
* * * *
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PROBLEM 4:
If sin 𝑎 = 1 − 𝑥 ) , then csc 𝑎 is most close to:
A. B. C. D.
1 − 𝑥) 9 :;9 < : :;9 < 9 :=9
?
B.
A?
C.
>A
D.
>?
@ > ? A
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PROBLEM 6: For natural functions with angles between 90° and 180°, which of the following statements is true: A. The tangent is positive B. The cotangent is positive C. The cosine is negative D. The sine is negative
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PROBLEM 7: The inverse of the natural cosecant function is best represented as: A. Secant B. Sine C. Cosine D. Tangent
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PROBLEM 8: Given the defined triangle, the trigonometric ratio for cotangent is best represented as:
A. cot 𝜃 = B. cot 𝜃 = C. cot 𝜃 = D. cot 𝜃 =
* ' ( ) M ) * )
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PROBLEM 9: '
If cos 𝜃 = , the ratio for cosecant is most close to: &
A. csc 𝜃 = B. csc 𝜃 =
& ( & '
C. csc 𝜃 =
&
D. csc 𝜃 =
&
) *
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PROBLEM 10: )
Given that sin 𝜃 = and cos 𝜃 = '
A. cot 𝜃 = B. cot 𝜃 = C. cot 𝜃 = D. cot 𝜃 =
* '
, the cot 𝜃 is best represented as:
* ' ' ) * ' * )
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PROBLEM 11: If sin 𝑎 = 𝑥, then sec 𝑎 is most close to:
A. B. C. D.
1 − 𝑥) 9 :;9 < : :;9 < 9 :=9
