What is the solution for θ in the equation y - xtanθ = z/cosθ?

Thread starter ohaiyo88
Start date Nov 25, 2011
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Angle

In summary, solving for θ in an x, y, z equation allows us to determine the exact angle at which two lines intersect or the orientation of a three-dimensional object. This is done using trigonometric functions such as sine, cosine, and tangent, as well as the given values of x, y, and z in the equation. Common mistakes include using the wrong trigonometric function and not converting between degrees and radians. There can be multiple solutions for θ in an x, y, z equation, which is useful in various real-world applications such as architecture, physics, and navigation.

Nov 25, 2011

ohaiyo88

y - xtanθ = z/cosθ

Find θ in terms of x,y,z
equation seems so simple, but can't do it

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Nov 25, 2011

ehild

Homework Helper

What did you try?ehild

Nov 25, 2011

ohaiyo88

cant do it. pls help. it's urgent

Nov 25, 2011

ehild

Homework Helper

You can use the relation between cos(θ) and than(θ):
1/cos(θ)=sqrt(1+tan²(θ)).

ehild

What is the purpose of solving for θ in an x, y, z equation?

The variable θ represents an angle in a three-dimensional coordinate system. Solving for θ allows us to determine the exact angle at which two lines intersect or the orientation of a three-dimensional object.

How do I solve for θ in an x, y, z equation?

To solve for θ, you will need to use trigonometric functions such as sine, cosine, and tangent. These functions relate the sides of a triangle to its angles and can be used to solve for unknown angles. You will also need to use the given values of x, y, and z in the equation to determine the correct trigonometric function to use.

What are the common mistakes made when solving for θ in an x, y, z equation?

One common mistake is using the wrong trigonometric function. Make sure to carefully examine the given values and determine which function is necessary. Another common mistake is not properly converting between degrees and radians. Make sure to use the correct unit of measurement when solving for θ.

Can there be more than one solution for θ in an x, y, z equation?

Yes, there can be multiple solutions for θ in an x, y, z equation. This occurs when there are multiple possible angles that satisfy the given values in the equation. It is important to carefully examine the problem and determine if there are multiple solutions, and if so, which ones are relevant.

What real-world applications require solving for θ in an x, y, z equation?

Solving for θ in an x, y, z equation is useful in various fields such as engineering, physics, and astronomy. It can be used to calculate the angles of intersecting beams in architecture, the orientation of objects in space, and the trajectory of projectiles in physics problems. It is also commonly used in navigation and surveying to determine angles and distances.