Mixed Practice Trigonometric Ratios

  • 9th Grade
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Cierra Henderson, MBA |
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Cierra is an educational consultant and curriculum developer who has worked with students in K-12 for a variety of subjects including English and Math as well as test prep. She specializes in one-on-one support for students especially those with learning differences. She holds an MBA from the University of Massachusetts Amherst and a certificate in educational consulting from UC Irvine.
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Quizzes Created: 8156 | Total Attempts: 9,588,805
| Attempts: 18 | Questions: 20 | Updated: Jan 19, 2026
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Question 1 / 21
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1) If sin(θ) = 3/5, then csc(θ) = ?

Explanation

Cosecant is the reciprocal of sine, so 5 over 3.

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About This Quiz
Mixed Practice Trigonometric Ratios - Quiz

Ready for a challenge that mixes it all together? In this quiz, you’ll solve problems that blend direct calculation, reciprocal identities, triangle applications, and graph reasoning. Take this quiz to prove you’ve mastered reciprocal ratios from every angle.

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2) If cos(θ) = 12/13, then sec(θ) = ?

Explanation

Secant is the reciprocal of cosine, so 13 over 12.

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3) If tan(θ) = 7/24, then cot(θ) = ?

Explanation

Cotangent is the reciprocal of tangent, so 24 over 7.

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4) The reciprocal of tangent is:

Explanation

The reciprocal of tangent is cotangent.

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5) If cot(θ) = 5/12, then tan(θ) = ?

Explanation

The reciprocal of cotangent is tangent, so 12 over 5.

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6) If sec(θ) = 17/8, then cos(θ) = ?

Explanation

The reciprocal of secant gives cosine 8 over 17.

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7) If csc(θ) = 13/12, then sin(θ) = ?

Explanation

The reciprocal of cosecant gives sine 12 over 13.

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8) In a right triangle, if the side opposite θ is 8 and the hypotenuse is 17, what is sin(θ)?

Explanation

Opposite over hypotenuse gives sine as 8 over 17.

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9) In a right triangle, the adjacent side to θ is 12 and the hypotenuse is 13. What is cos(θ)?

Explanation

Adjacent over hypotenuse gives cosine as 12 over 13.

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10) The reciprocal of cosine is:

Explanation

The reciprocal of cosine is secant.

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11) If cos(θ) = -4/5, then sec(θ) = ?

Explanation

Take the reciprocal of −4/5 to get secant −5/4.

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12) If sin(θ) = -12/13, then csc(θ) = ?

Explanation

Take the reciprocal of −12/13 to get cosecant −13/12.

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13) If tan(θ) = 3/4, then sin(θ) = ?

Explanation

A 3–4–5 triangle matches the ratio 3/4 for tangent, so sine is 3/5.

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14) For the triangle in Q15, cos(θ) = ?

Explanation

Cosine is adjacent over hypotenuse, so 40 over 41.

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15) Which function is undefined whenever cosine = 0?

Explanation

Tangent (and also secant) is undefined where cosine is zero; the expected choice here is tangent.

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16) Which reciprocal pair matches correctly?

Explanation

The correct reciprocal pair is tangent and cotangent.

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17) Which function is undefined whenever sine = 0?

Explanation

Cosecant is undefined where sine is zero.

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18) If tan(θ) = 3/4, then cos(θ) = ?

Explanation

With the same triangle, cosine is 4/5.

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19) In a right triangle, if one leg is 9, the other leg is 40, and the hypotenuse is 41, then sin(θ) opposite the side 9 is:

Explanation

Sine is opposite over hypotenuse, so 9 over 41.

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20) For the triangle in Q15, csc(θ) = ?

Explanation

Cosecant is the reciprocal of sine, so 41 over 9.

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Cierra Henderson |MBA |
K-12 Expert
Cierra is an educational consultant and curriculum developer who has worked with students in K-12 for a variety of subjects including English and Math as well as test prep. She specializes in one-on-one support for students especially those with learning differences. She holds an MBA from the University of Massachusetts Amherst and a certificate in educational consulting from UC Irvine.
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If sin(θ) = 3/5, then csc(θ) = ?
If cos(θ) = 12/13, then sec(θ) = ?
If tan(θ) = 7/24, then cot(θ) = ?
The reciprocal of tangent is:
If cot(θ) = 5/12, then tan(θ) = ?
If sec(θ) = 17/8, then cos(θ) = ?
If csc(θ) = 13/12, then sin(θ) = ?
In a right triangle, if the side opposite θ is 8 and the...
In a right triangle, the adjacent side to θ is 12 and the...
The reciprocal of cosine is:
If cos(θ) = -4/5, then sec(θ) = ?
If sin(θ) = -12/13, then csc(θ) = ?
If tan(θ) = 3/4, then sin(θ) = ?
For the triangle in Q15, cos(θ) = ?
Which function is undefined whenever cosine = 0?
Which reciprocal pair matches correctly?
Which function is undefined whenever sine = 0?
If tan(θ) = 3/4, then cos(θ) = ?
In a right triangle, if one leg is 9, the other leg is 40, and the...
For the triangle in Q15, csc(θ) = ?
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