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

• Fresh4Christ
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.
Fresh4Christ
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

Show some work. Hint: look up some trig identities and start playing around.

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

Hint: divide everything by cos A first.

Ok, in fact, the book does skip some steps:
$$0 = 3[\cos (35 ^ o) \cos A - \sin(35 ^ o) - \sin A] - \cos A$$
Now divide both sides by cos A, we have:
$$0 = \frac{3[\cos (35 ^ o) \cos A - \sin(35 ^ o) - \sin A] - \cos A}{\cos A} = 3 \cos (35 ^ o) - 1 - 3 \sin (35 ^ o) \tan A$$
$$\Leftrightarrow 3 \cos (35 ^ o) - 1 = 3 \sin (35 ^ o) \tan A$$
Divide both sides by 3, we have:
$$\Leftrightarrow \cos (35 ^ o) - \frac{1}{3} = \sin (35 ^ o) \tan A$$
Now, divide everything by sin(35o), we have:
$$\Leftrightarrow \frac{\cos (35 ^ o) - \frac{1}{3}}{\sin (35 ^ o)} = \tan A$$
Can you get this? :)

Last edited:
Yes, thank you very much

VietDao, how did you get your second line?

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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