Direct Calculation from Triangles

Reviewed by Editorial Team
The ProProfs editorial team is comprised of experienced subject matter experts. They've collectively created over 10,000 quizzes and lessons, serving over 100 million users. Our team includes in-house content moderators and subject matter experts, as well as a global network of rigorously trained contributors. All adhere to our comprehensive editorial guidelines, ensuring the delivery of high-quality content.
Learn about Our Editorial Process
| By Thames
T
Thames
Community Contributor
Quizzes Created: 7060 | Total Attempts: 9,520,935
| Questions: 20 | Updated: Oct 15, 2025
Please wait...
Question 1 / 20
0 %
0/100
Score 0/100
1) 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
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)
We’ll put your name on your report, certificate, and leaderboard.
2) 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
3) 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
4) 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
5) 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
6) If csc θ = 17/8, then sin θ = ?

Explanation

Since csc θ is 17/8, sin θ is 8/17.

Submit
7) If sec θ = 25/24, then cos θ = ?

Explanation

Since sec θ is 25/24, cos θ is 24/25.

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

Explanation

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

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 csc θ = 2, then sin θ = ?

Explanation

If csc θ is 2, then sin θ is 1/2.

Submit
11) If sec θ = 10, then cos θ = ?

Explanation

If sec θ is 10, then cos θ is 1/10.

Submit
12) 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
13) If csc θ = 41/40, then sin θ = ?

Explanation

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

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 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
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 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
19) 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
20) 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
View My Results
Cancel
  • All
    All (20)
  • Unanswered
    Unanswered ()
  • Answered
    Answered ()
If sin θ = 5/13, then csc θ = ?
If cos θ = 8/17, then sec θ = ?
If csc θ = -25/7, then sin θ = ?
A right triangle has legs 8 and 15, and hypotenuse 17. Find sec...
If csc θ = 25/7, which of the following cannot be a...
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 cos θ = 3/5, then sec θ = ?
If csc θ = 2, then sin θ = ?
If sec θ = 10, then cos θ = ?
In a right triangle, cos θ = 12/13. Find csc θ.
If csc θ = 41/40, then sin θ = ?
If tan θ = 5/12, which of the following cannot be a...
If cot θ = 5/12, then tan θ = ?
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 9 and 12, and hypotenuse 15. Find csc...
In a right triangle, tan θ = 3/4. Find csc θ.
If sec θ = 13/5, which of the following cannot be a...
Alert!

Back to Top Back to top
Advertisement