Solve for x with a trigonometric function

In summary: Again, I think it would be helpful to show your work for the complete pattern. Sorry. My mistake. See the Edit above. Again, I think it would be helpful to show your work for the complete pattern.
  • #1
ver_mathstats
260
21
Homework Statement
Solve for x.
Relevant Equations
sin(3x)= -1/2
Homework Statement: Solve for x.
Homework Equations: sin(3x)= -1/2

sin(3x) = -1/2

3x = sin-1(-1/2)

3x = -π/6

x = -π/18

x = -π/18 + 2π/3 = 11π/18

11π/18 + 2π/3 = 23π/18

11π/18 + (2π(4))/3 = 35π/18

The solutions I obtained were 23π/18 and 35π/18. Are these correct? I'm not entirely sure if I did this problem correctly. Thank you.
 
Physics news on Phys.org
  • #2
What about a solution or solutions where the angle 3x is in the 3rd quadrant? (You found the solution when 3x is in the 4th quadrant). ## \\ ## Your solutions are incomplete, even for the 4th quadrant. You need to let ##3x=\theta+n (2 \pi) ##, where ## n ## is any integer. You found ## \theta ## for the 4th quadrant, etc., but it helps to be more systematic. Otherwise, you don't get the complete set.
 
  • #3
Charles Link said:
What about a solution or solutions where the angle 3x is in the 3rd quadrant? (You found the solution when 3x is in the 4th quadrant). ## \\ ## Your solutions are incomplete, even for the 4th quadrant. You need to let ##3x=\theta+n (2 \pi) ##, where ## n ## is any integer. You found ## \theta ## for the 4th quadrant, etc., but it helps to be more systematic. Otherwise, you don't get the complete set.
Yes I can see where I went wrong. I got the solutions 7π/18, 11π/18, 19π/18, 23π/18, 31π/18, 35π/18 after looking it over. Thank you.
 
  • #4
Still incomplete. And please show your work. And I don't think I agree with the ## \frac{7 \pi}{18} ##. Edit: My mistake. OP has it correct. As @PAllen mentions below though, the OP needs to include the negative x values that come from negative integer ##n ## in ## 3x=\theta+n(2 \pi) ##.
 
Last edited:
  • #5
Charles Link said:
And I don't think I agree with the ## \frac{7 \pi}{18} ##.
Looks fine to me. Also, his last set of solutions looks fine as the beginning of an obvious pattern that is complete (except for negative x values).
 
Last edited:
  • Like
Likes Charles Link
  • #6
PAllen said:
Looks fine to me. Also, his last set of solutions looks fine as the beginning of an obvious pattern that is complete (except for negative x values).
Sorry. My mistake. See the Edit above.
 

FAQ: Solve for x with a trigonometric function

1. What is a trigonometric function?

A trigonometric function is a mathematical function that relates an angle of a right triangle to the ratios of the lengths of its sides. The most commonly used trigonometric functions are sine, cosine, and tangent.

2. How do you solve for x with a trigonometric function?

To solve for x with a trigonometric function, you will need to use algebraic manipulation and trigonometric identities to isolate the trigonometric function and its angle. Once the function and angle are isolated, you can use a calculator or tables to find the value of x.

3. Can trigonometric functions be used to solve for x in non-right triangles?

No, trigonometric functions can only be used to solve for x in right triangles. For non-right triangles, you will need to use other methods such as the law of sines or the law of cosines.

4. What are some common mistakes when solving for x with trigonometric functions?

Some common mistakes when solving for x with trigonometric functions include forgetting to use the correct inverse function, not converting angles to the correct unit (degrees or radians), and not checking for extraneous solutions.

5. Are there any tips for solving trigonometric functions with ease?

Some tips for solving trigonometric functions with ease include memorizing common trigonometric identities, practicing regularly, and breaking down the problem into smaller steps. It is also important to double-check your work and pay attention to units when using a calculator.

Similar threads

Replies
1
Views
1K
Replies
5
Views
2K
Replies
15
Views
1K
Replies
1
Views
1K
Replies
8
Views
2K
Replies
8
Views
2K
Replies
11
Views
859
Replies
10
Views
1K
Back
Top