Can you tell me why my trig functions aren't working?

In summary: The two solutions obtained applying the law of sines cannot be distinguished easily by algebraic means. This is more of a geometric problem and as such, it is always best to have a diagram handy. The diagram would indicate that the solution is 29.44 and not 79.44. Remember, with the law of sines, we are either adding or subtracting angles to get the correct answer. In this case, we are subtracting. I hope this helps.In summary, the conversation discusses using the law of cosines and the law of sines to find the third side and remaining angles of a triangle. The calculated results for the angles were 79.4 and 29.4,
  • #1
mrhingle
21
0
I am given two sides of a triangle and the angle in/between them: 9 in/s and 4.5 in/s at 50 degrees. I am using the Law of cosines to get the third side which is 7.013 in/s. I then used the law of sine to find the two remaining angles. I have continually gotten 79.4 for one angle and 29.4 for the other. 80 + 30 + 50 = 160. I can't figure out what I am doing wrong. Will someone please tell me the correct solutions, it's killing me. I've been attempting this for 1 hour with consistent results. Thanks, I'm a dummy...
 
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  • #2
the angle that you think is 79.4 is actually 180 MINUS 79.4 and I have no idea where you got 29.4 for anything but once you change the 79.4 maybe you'll get the other one right too.
 
  • #3
Show your calculations.
 
  • #4
Calculations:
[itеx] v(a)^2 = 9^2 +4.5^2 - 2 * 4.5 * 9 cos (50)
v(a) = 7.013

7.013/Sin(50) = 4.5/ Sin(alpha)
alpha = 29.44

7.013/sin(50) = 9/sin(beta)
beta = 79.44
[/itеx]
 
  • #5
Calculations:
[itеx] v(a)^2 = 9^2 +4.5^2 - 2 * 4.5 * 9 cos (50)
v(a) = 7.013

7.013/Sin(50) = 4.5/ Sin(alpha)
alpha = 29.44

7.013/sin(50) = 9/sin(beta)
beta = 79.44
[/itеx]
 
  • #6
Angle between 9 and 7.013 is more than 90 degrees. You can verify this by using cosine rule to find the angle between them.
 
  • #7
used the law of cosines. still got 29.44
 
  • #8
Sorry. Use cosine rule to find the angle between 4.5 and 7.013.
 
  • #9
79.44
 
  • #10
Is there no negative sign in the answer?
 
  • #11
nope
 
  • #12
the inverse is negative
 
  • #13
The angle beta could be either 79.44 or (180 - 79.44), as determined by the law of sines.
 
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  • #14
what does that mean? I thought this was a law? Do you have to use the same law for all angles?
 
  • #16
mrhingle said:
what does that mean? I thought this was a law? Do you have to use the same law for all angles?

In the second quadrant cosine is negative. So whatever angle you get, you have to write it as 180-θ
 
  • #17
I see.. but when you use the laws to obtain angle B, why do I get 79.44? Makes me doubt the laws. When do you have to subtract the angle from 180. Is there a rule that makes since of this?
 
  • #18
mrhingle said:
what does that mean? I thought this was a law? Do you have to use the same law for all angles?
sin(θ) = sin(180 - θ)
 
  • #19
mrhingle said:
I see.. but when you use the laws to obtain angle B, why do I get 79.44? Makes me doubt the laws. When do you have to subtract the angle from 180. Is there a rule that makes since of this?

It how the law was derived.
In this example one of the common perperdicular line(common to adjacent angles) is outside the triangle.
Thus we are measuring the external angle.

Thanks for bring it up. I think that it is just plug and chug.

Add: It's really prove that a diagram or a sketch is very helpful as in tool of problem solving, IDEA(D for drawing) from Richard Wolfson's book.
 
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  • #20
mrhingle said:
I see.. but when you use the laws to obtain angle B, why do I get 79.44? Makes me doubt the laws. When do you have to subtract the angle from 180. Is there a rule that makes since of this?

No the laws are correct. There are two possible solutions obtained applying the law of sines to this problem. Both solutions satisfy the law of sines. Applying the law of cosines to the other angles of the triangle clinches the results. In fact, applying the law of cosines delivers a unique solution.
 

FAQ: Can you tell me why my trig functions aren't working?

1) Why are my trig functions giving me incorrect values?

There could be several reasons for this. Some common mistakes include using the wrong units (degrees instead of radians or vice versa), forgetting to convert from degrees to radians, or using the wrong function (such as using sine instead of cosine). Double check your calculations and make sure you are using the correct function for the problem.

2) Why am I getting an error message when I try to use trig functions?

One possible reason for this is that you are not using the correct syntax for the programming language or software you are using. Check the documentation or consult a reference guide to make sure you are using the proper syntax for the specific function you are trying to use.

3) How do I know which trig function to use for a specific problem?

The choice of trig function depends on the given information and the problem you are trying to solve. For example, if you have the length of the hypotenuse and the adjacent side of a right triangle, you would use cosine. If you have the length of the hypotenuse and the opposite side, you would use sine. Analyze the given information and determine which function would be most appropriate to use.

4) Can rounding errors affect the accuracy of my trig functions?

Yes, rounding errors can affect the accuracy of your trig functions. If you are using a calculator or a computer program to calculate trigonometric values, it is important to make sure you are using enough significant figures in your calculations to avoid significant rounding errors. In some cases, it may be necessary to round your final answer to the appropriate number of significant figures.

5) How can I check my work when using trig functions?

One way to check your work is to use a calculator or computer program to confirm your calculations. You can also use the properties and identities of trig functions to verify your results. Additionally, it is always a good idea to double check your work and make sure you are using the correct units and function for the given problem.

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