Solving Trig Equations: Understanding Degrees and Terminal Arm Usage

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In summary, the basic steps for solving trigonometric equations are: 1) identify the type of equation, 2) use algebra to isolate the trigonometric function, 3) use inverse trigonometric functions to solve for the variable, and 4) check the solution by substituting it back into the original equation. When solving trigonometric equations, it is important to use the correct unit of measurement (degrees or radians) for the given problem. The terminal arm is used in trigonometry to determine the direction and magnitude of an angle, as well as to help visualize the values of the trigonometric functions. Trigonometric equations can have more than one solution due to the periodic nature of trigonometric functions
  • #1
Nelo
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Homework Statement



I don't understand how to solve for these, I will post 3.

d) [sqrt]2sin x + 1 = 0 (sqrt only over the 2)
e) 2cos x - [sqrt]3 = 0
f) 2sinx +[sqr]3 = 0

Esentially, I don't understand how to get the degrees. I don't get how you use the terminal arm to predict the degrees, etc.

Can anyone help?



Homework Equations





The Attempt at a Solution



1 / [sqrt]2

sin inverse of that is 30 degrees.

which is pi over 6.

How do i get the second one? how do i know? etc
 
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  • #2
Nelo said:
d) [sqrt]2sin x + 1 = 0 (sqrt only over the 2)
e) 2cos x - [sqrt]3 = 0
f) 2sinx +[sqr]3 = 0

I am assuming you are finding from 0 to 2pi.

Nelo said:

The Attempt at a Solution



1 / [sqrt]2

sin inverse of that is 30 degrees.

which is pi over 6.

How do i get the second one? how do i know? etc

For the three you are doing the same thing, making sinx or cosx the subject of the formula and then taking the inverse function of it.

The first one you did partially right

sinx = 1/√2 and x=sin-1(1/√2)

Check back on your calculator for what value this is.

When you get that what quadrant is sine positive in?
 
  • #3
Nelo said:

Homework Statement



I don't understand how to solve for these, I will post 3.

d) [sqrt]2sin x + 1 = 0 (sqrt only over the 2)
e) 2cos x - [sqrt]3 = 0
f) 2sinx +[sqr]3 = 0

Esentially, I don't understand how to get the degrees. I don't get how you use the terminal arm to predict the degrees, etc.

Can anyone help?



Homework Equations





The Attempt at a Solution



1 / [sqrt]2

sin inverse of that is 30 degrees.

which is pi over 6.

How do i get the second one? how do i know? etc

Write sqrt(2) instead of [sqrt]2, etc; that way, you don't have to make statements like "sqrt only over the 2". Anyway, if you know elementary Geometry, you should be able to see what angles give you sin(x) = -1/sqrt(2), cos(x) = 3/sqrt(2) and sin(x) = -sqrt(3)/2. I realize that Geometry may not be taught anymore in schools, in which case you can do a Google search on something like "sines of special angles" to find some material.

RGV
 
  • #4
4f) cosx =2sincosx

How do you solve this?

The only thing i see is

..cosx - cosx- = 2sin

is that wrong?

does that mean cos is 0 and sin is 90+90 = 180 degrees?
 
  • #5
Nelo said:
4f) cosx =2sincosx

How do you solve this?

The only thing i see is

..cosx - cosx- = 2sin

is that wrong?

does that mean cos is 0 and sin is 90+90 = 180 degrees?

bring the cosx on the left side to the right side and then factor out the cosx.
 
  • #6
Does that not equal the exact same thing? cos is 0 and sin is 180?
 
  • #7
Nelo said:
Does that not equal the exact same thing? cos is 0 and sin is 180?

You mean x=0, x=180? if so, by putting x=0 into the equation you will see that it is not a solution.
 

FAQ: Solving Trig Equations: Understanding Degrees and Terminal Arm Usage

What are the basic steps for solving trigonometric equations?

The basic steps for solving trigonometric equations are:

  • 1. Identify the type of equation (sine, cosine, tangent, etc.)
  • 2. Use algebra to isolate the trigonometric function.
  • 3. Use inverse trigonometric functions to solve for the variable.
  • 4. Check your solution by substituting it back into the original equation.

How do I know when to use degrees or radians?

When solving trigonometric equations, it is important to use the correct unit of measurement (degrees or radians) for the given problem. In general, degrees are used when measuring angles in real-life situations, such as navigation or construction. Radians are used when dealing with more complex mathematical concepts, such as derivatives or integrals. When in doubt, check the instructions or ask your teacher for clarification.

What is the terminal arm and how is it used in trigonometry?

The terminal arm is the arm of an angle that starts at the initial side and rotates counterclockwise to form the angle. In trigonometry, the terminal arm is used to determine the direction and magnitude of the angle, as well as to help visualize the values of the trigonometric functions.

Can trigonometric equations have more than one solution?

Yes, trigonometric equations can have more than one solution. This is due to the periodic nature of trigonometric functions, which means that they repeat their values after a certain interval. Therefore, when solving trigonometric equations, it is important to check for all possible solutions within the given interval.

How can I check if my solution is correct?

To check if your solution to a trigonometric equation is correct, you can substitute the value back into the original equation and see if it satisfies the equation. If the substitution results in a true statement, then your solution is correct. If it results in a false statement, then there may be a mistake in your calculations and you should double-check your work.

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