Solving a Trigonometry Problem with Tan A and Tan B

In summary, the equations y=2x and 3y=x-1 represent lines L1 and L2 respectively on the same set of axes. The scales on both axes are equal and the angles L1 and L2 make with the positive x-axis are A and B respectively. The value of tan A is 2 and the value of tan B can be found by rearranging the equation 3y=x-1 into the standard form for a straight line and solving for the slope, which is equal to tan B.
  • #1
Davidmb19
21
0

Homework Statement


The lines L1 and L2 with equations y=2x and 3y=x-1 respectively,are drawn on the same set of axes. Given that the scales are the same on both axes and that the angle L1 and L2 make with the positive x-asis are A and B respectively,

write down the value of Tan A and the value of Tan B

Homework Equations


Tan=O/A

The Attempt at a Solution



I've figured out tanA which is 2. Why? It doesn't matter what value of x you substitute into L1 you'll always get 2 when you do O which is Y divide by A which is X. I'm using tan=o/a. But, I do not know how to get tan B; it isn't the same thing.
 
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  • #2
The general (or standard) equation for a straight line is y = mx + c where

m is the slope = Δy/Δx = Tanθ
and c is a constant.

So comparing that with y=2x it's clear that m=2 (and c=0).

I suggest you rearrange the other equation (3y=x-1) into the standard form for a straight line and work out the slope m.
 
  • #3
Δy/Δx = Tanθ << Ahh you're right. I never noticed even though I used the same method.Silly me. Thanks
 

FAQ: Solving a Trigonometry Problem with Tan A and Tan B

1. What is the formula for solving a trigonometry problem using tan A and tan B?

The formula for solving a trigonometry problem using tan A and tan B is: tan(A + B) = (tan A + tan B) / (1 - tan A * tan B)

2. How do I determine the value of tan A and tan B in a trigonometry problem?

To determine the value of tan A and tan B, you will need to know the measurements of the triangle's sides and angles. You can use the tangent ratio, which is opposite side over adjacent side, to find the values of tan A and tan B.

3. Can I use tan A and tan B to solve any type of trigonometry problem?

No, tan A and tan B can only be used to solve problems involving right triangles. For other types of triangles, you will need to use different trigonometric ratios such as sine and cosine.

4. What is the difference between using tan A and tan B and using the Pythagorean theorem to solve a trigonometry problem?

The Pythagorean theorem can only be used to solve for the sides and hypotenuse of a right triangle, while using tan A and tan B allows you to solve for angles as well. Additionally, the Pythagorean theorem relies on the relationship between the sides of a triangle, while tan A and tan B rely on the ratios of the triangle's sides and angles.

5. Are there any special cases or restrictions when using tan A and tan B to solve a trigonometry problem?

Yes, there are a few special cases to keep in mind. First, tan A and tan B cannot be used to solve for the value of the hypotenuse, as it is not involved in the tangent ratio. Additionally, the angle A and angle B must be complementary (add up to 90 degrees) in order for the formula to work.

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