Trig 0 = 3[cos(35)*cos(A) - sin(35)*sin(A)] - cos(A)

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In summary, the problem is given as 0 = 3[cos(35)*cos(A) - sin(35)*sin(A)] - cos(A) where A is alpha and the goal is to find the value of A. By dividing both sides by cos A and then further manipulating the equations using trigonometric identities, we can get the simplified form of tan(A) = [cos(35) - 1/3] / sin(35). The book skips some steps, but by dividing everything by cos A and then sin(35), we can reach the final form.
  • #1
Fresh4Christ
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I have the problem:

0 = 3[cos(35)*cos(A) - sin(35)*sin(A)] - cos(A)
where A is alpha...my unknown degree.

somehow that turns into this:

tan(A) = [cos(35) - 1/3] / sin(35)

I am not drawing the connection or seeing how that is happening...

Could you help? THANKS
 
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  • #2
Show some work. Hint: look up some trig identities and start playing around.
 
  • #3
i tried... this isn't a homework problem... its in the textbook. It jumps from that first step to the next one just saying "Then we can see:" ... and I can't see that
 
  • #4
Hint: divide everything by cos A first.
 
  • #5
Ok, in fact, the book does skip some steps:
[tex]0 = 3[\cos (35 ^ o) \cos A - \sin(35 ^ o) - \sin A] - \cos A[/tex]
Now divide both sides by cos A, we have:
[tex]0 = \frac{3[\cos (35 ^ o) \cos A - \sin(35 ^ o) - \sin A] - \cos A}{\cos A} = 3 \cos (35 ^ o) - 1 - 3 \sin (35 ^ o) \tan A[/tex]
[tex]\Leftrightarrow 3 \cos (35 ^ o) - 1 = 3 \sin (35 ^ o) \tan A[/tex]
Divide both sides by 3, we have:
[tex]\Leftrightarrow \cos (35 ^ o) - \frac{1}{3} = \sin (35 ^ o) \tan A[/tex]
Now, divide everything by sin(35o), we have:
[tex]\Leftrightarrow \frac{\cos (35 ^ o) - \frac{1}{3}}{\sin (35 ^ o)} = \tan A[/tex]
Can you get this? :)
 
Last edited:
  • #6
Yes, thank you very much
 
  • #7
VietDao, how did you get your second line?
 
  • #8
He divided both sides by 3, if you mean the 2nd part of that line, He just added 3 sin 35 tan A to both sides.
 

1. What is Trig 0?

Trig 0 is a mathematical expression that represents the value of the trigonometric function at 0 degrees.

2. What does the number 3 represent in "Trig 0 = 3[cos(35)*cos(A) - sin(35)*sin(A)] - cos(A)"?

The number 3 is a coefficient that is multiplied to the trigonometric expression to produce the final value of Trig 0.

3. How do you solve for A in the equation "Trig 0 = 3[cos(35)*cos(A) - sin(35)*sin(A)] - cos(A)"?

To solve for A, you can use algebraic manipulation and trigonometric identities to isolate the variable on one side of the equation and solve for its value.

4. What is the significance of the values 35 and A in the equation "Trig 0 = 3[cos(35)*cos(A) - sin(35)*sin(A)] - cos(A)"?

The value 35 represents the angle in degrees at which the trigonometric function is being evaluated, while A represents an unknown angle that can be solved for using the given equation.

5. Can this equation be used to solve for any trigonometric function at 0 degrees?

Yes, this equation can be used to solve for any trigonometric function at 0 degrees as long as the appropriate coefficients, angles, and trigonometric identities are used.

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