Direct Calculation from Triangles

  • 10th Grade
Reviewed by Cierra Henderson
Cierra Henderson, MBA |
K-12 Expert
Review Board Member
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.
 , MBA
By Thames
T
Thames
Community Contributor
Quizzes Created: 8156 | Total Attempts: 9,588,805
| Attempts: 40 | Questions: 20 | Updated: Jan 19, 2026
Please wait...
Question 1 / 21
🏆 Rank #-- ▾
Score 0/100

1) If csc θ = -25/7, then sin θ = ?

Explanation

Sine is the reciprocal of cosecant. Since csc θ is −25/7, sin θ is −7/25.

Submit
Please wait...
About This Quiz
Direct Calculation From Triangles - Quiz

Are you ready to put your triangle skills to the test? In this quiz, you’ll practice moving between sine, cosine, tangent, and their reciprocals—cosecant, secant, and cotangent—by working directly with right triangles. Take this quiz to sharpen your ability to compute reciprocal ratios quickly and confidently.

2)

What first name or nickname would you like us to use?

You may optionally provide this to label your report, leaderboard, or certificate.

2) If csc θ = 17/8, then sin θ = ?

Explanation

Since csc θ is 17/8, sin θ is 8/17.

Submit

3) If sec θ = 25/24, then cos θ = ?

Explanation

Since sec θ is 25/24, cos θ is 24/25.

Submit

4) If sin θ = -12/13, then csc θ = ?

Explanation

Since sin θ is −12/13, csc θ is −13/12.

Submit

5) If csc θ = 2, then sin θ = ?

Explanation

If csc θ is 2, then sin θ is 1/2.

Submit

6) If sec θ = 10, then cos θ = ?

Explanation

If sec θ is 10, then cos θ is 1/10.

Submit

7) If sin θ = 5/13, then csc θ = ?

Explanation

Cosecant is the reciprocal of sine. Since sin θ is 5/13, csc θ is 13/5.

Submit

8) If cos θ = 8/17, then sec θ = ?

Explanation

Secant is the reciprocal of cosine. Since cos θ is 8/17, sec θ is 17/8.

Submit

9) If cos θ = 3/5, then sec θ = ?

Explanation

Since cos θ is 3/5, sec θ is 5/3.

Submit

10) If cot θ = 5/12, then tan θ = ?

Explanation

Cotangent and tangent are reciprocals. If cot θ is 5/12, then tan θ is 12/5.

Submit

11) If csc θ = 41/40, then sin θ = ?

Explanation

If csc θ is 41/40, then sin θ is 40/41.

Submit

12) If sec θ = 13/5, which of the following cannot be a trigonometric ratio in the same right triangle?

Explanation

If sec θ is 13/5, then cos θ is 5/13 and sin θ must be 12/13 (or negative, by quadrant). So sin θ = 5/13 doesn’t match that triangle.

Submit

13) In a right triangle, cos θ = 12/13. Find csc θ.

Explanation

With cos θ = 12/13 (a 5–12–13 triangle), sin θ is 5/13, so csc θ is 13/5.

Submit

14) If tan θ = 5/12, which of the following cannot be a trigonometric ratio in the same right triangle?

Explanation

For tan θ = 5/12 (the 5–12–13 triangle), csc θ should be 13/5, not 12/5. So 12/5 is the one that can’t occur.

Submit

15) If csc θ = 25/7, which of the following cannot be a trigonometric ratio in the same right triangle?

Explanation

From csc θ = 25/7 we get sin θ = 7/25 and cos θ = 24/25 (valid). A value like cos θ = 25/24 is bigger than 1, so it can’t happen.

Submit

16) In a right triangle, sin θ = 15/17. Find sec θ.

Explanation

With sin θ = 15/17, cos θ is 8/17, so sec θ is 17/8.

Submit

17) A right triangle has legs 7 and 24, and hypotenuse 25. Find cot θ if θ is the angle opposite the side of length 7.

Explanation

Cotangent is adjacent over opposite. With opposite 7 and adjacent 24, cot θ is 24/7.

Submit

18) A right triangle has legs 8 and 15, and hypotenuse 17. Find sec θ if θ is the angle opposite the side of length 8.

Explanation

In the 8–15–17 triangle (θ opposite 8), cos θ is 15/17, so sec θ is 17/15.

Submit

19) A right triangle has legs 9 and 12, and hypotenuse 15. Find csc θ if θ is the angle opposite the side of length 9.

Explanation

With sides 9–12–15 and θ opposite 9, sin θ is 3/5, so csc θ is 5/3.

Submit

20) In a right triangle, tan θ = 3/4. Find csc θ.

Explanation

tan θ = 3/4 matches a 3–4–5 triangle, so sin θ is 3/5 and csc θ is 5/3.

Submit
×
Saved
Thank you for your feedback!
View My Results
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.
Cancel
  • All
    All (20)
  • Unanswered
    Unanswered ()
  • Answered
    Answered ()
If csc θ = -25/7, then sin θ = ?
If csc θ = 17/8, then sin θ = ?
If sec θ = 25/24, then cos θ = ?
If sin θ = -12/13, then csc θ = ?
If csc θ = 2, then sin θ = ?
If sec θ = 10, then cos θ = ?
If sin θ = 5/13, then csc θ = ?
If cos θ = 8/17, then sec θ = ?
If cos θ = 3/5, then sec θ = ?
If cot θ = 5/12, then tan θ = ?
If csc θ = 41/40, then sin θ = ?
If sec θ = 13/5, which of the following cannot be a...
In a right triangle, cos θ = 12/13. Find csc θ.
If tan θ = 5/12, which of the following cannot be a...
If csc θ = 25/7, which of the following cannot be a...
In a right triangle, sin θ = 15/17. Find sec θ.
A right triangle has legs 7 and 24, and hypotenuse 25. Find cot...
A right triangle has legs 8 and 15, and hypotenuse 17. Find sec...
A right triangle has legs 9 and 12, and hypotenuse 15. Find csc...
In a right triangle, tan θ = 3/4. Find csc θ.
play-Mute sad happy unanswered_answer up-hover down-hover success oval cancel Check box square blue
Alert!