What is the relationship between angles in a 3D trigonometry problem?

  • Thread starter cosmo123
  • Start date
  • Tags
    3d Trig
In summary, the conversation discusses finding the value of angle a in terms of angles b and c in a 2d plane, with angle c being perpendicular to the plane and angle a being a projection of angle c onto the plane. The first attempt at a solution, using the lengths of edges in a cuboid, resulted in the incorrect equation of tan(a)=tan(b)tan(c). After further discussion, it was determined that the correct equation is tan a = sec b * tan c.
  • #1
cosmo123
24
0

Homework Statement


[PLAIN]http://img708.imageshack.us/img708/1344/trig.jpg
The angle c is separated from a 2d plane by angle b (perpendicular to the 2d plane). Angle a is angle c projected onto the 2d plane. What is a in terms of b and c?


Homework Equations





The Attempt at a Solution


I put the whole thing in a cuboid, used the lengths of the edges, and came to tan(a)=tan(b)tan(c). Can i just double check this with someone, because i don't trust my maths.
 
Last edited by a moderator:
Physics news on Phys.org
  • #2
It doesn't work. When b = 0, no matter what c is, your equation gives a = 0, which doesn't make sense as a = c when b = 0.

This seems more appropriate to me: tan a = tan c / cos b
 
  • #3
Yeah, it doesn't work, i probably should have checked some figures. I re-did it and i think i missed a 1. I got tan a = sqrt((tan b)^2 + 1) * tan c

=> tan a = sec b * tan c

so yes, youre completely right, thanks.
 

Related to What is the relationship between angles in a 3D trigonometry problem?

1. What is a "Simple 3d trig problem"?

A "Simple 3d trig problem" is a mathematical problem that involves using the principles of trigonometry to solve for unknown angles or sides in a three-dimensional space. It often involves visualizing and manipulating shapes in three dimensions to find the desired solution.

2. How is a "Simple 3d trig problem" different from a regular trigonometry problem?

A "Simple 3d trig problem" differs from a regular trigonometry problem in that it involves objects or shapes in three-dimensional space, rather than just two dimensions. This adds an extra layer of complexity to the problem, as it requires the use of three-dimensional geometry principles in addition to trigonometry concepts.

3. What are some common applications of "Simple 3d trig problems"?

"Simple 3d trig problems" have many real-world applications, such as in architecture, engineering, and navigation. For example, architects may use these problems to determine the angles and lengths of support beams in a building, while engineers may use them to calculate the trajectory of a plane or missile. They are also commonly used in video game and animation design to create realistic 3D environments.

4. What are the essential concepts and formulas needed to solve a "Simple 3d trig problem"?

To solve a "Simple 3d trig problem", you will need a solid understanding of trigonometric ratios (sine, cosine, and tangent), as well as the Pythagorean theorem and the concept of similar triangles. You will also need to know how to apply these concepts in a three-dimensional space, using formulas such as the Law of Cosines and the Law of Sines.

5. Can "Simple 3d trig problems" be solved using a calculator?

Yes, most "Simple 3d trig problems" can be solved using a calculator. However, it is essential to understand the concepts and formulas involved in the problem to use a calculator correctly. Additionally, some problems may require the use of trigonometric identities or inverse trigonometric functions, which may not be available on all calculators.

Similar threads

Exploring Equation of a Straight Line in 3D Space
    • Precalculus Mathematics Homework Help
Replies
17
Views
1K
I Solving Sub-Problem for OpenAI Lunar Lander v2: Seeking Advice
    • Mechanics
Replies
1
Views
769
What is the critical angle for a box to topple?
    • Introductory Physics Homework Help
Replies
2
Views
2K
At what angle should the bomb be released?
    • Introductory Physics Homework Help
Replies
4
Views
2K
Reflected Light at 3D Angle: Shift in Polarization
    • Optics
Replies
1
Views
3K
The volume of water gathered by a tilted paraboloid antenna
    • Calculus and Beyond Homework Help
Replies
10
Views
2K
A cuboid on an inclined plane - based on an Olympiad problem
    • Introductory Physics Homework Help
Replies
5
Views
1K
Multivariable Calculus: Geodesic problem
    • Calculus and Beyond Homework Help
Replies
1
Views
1K
Relationship between Polarizing Angle and Angle of internal reflection
    • Introductory Physics Homework Help
Replies
10
Views
16K
Finding the Angle Between a Vector in the yz-Plane and Another Vector
    • Precalculus Mathematics Homework Help
Replies
11
Views
7K

Hot Threads

Recent Insights

Back
Top