Find the Second Solution for sinx = A | Trigonometry Question

  • Thread starter DanielJackins
  • Start date
  • Tags
    Trigonometry
In summary, when x=7pi/23 is a solution of the equation sinx=A, A must be equal to sin(7pi/23) and the other solution in the interval [0,2pi] must be x=pi-7pi/23=16pi/23. The identity sinx=sin(pi-x) can be used to show the symmetry of sinx in the first and second quadrant, where two x values give the same A value. This means that when x is a solution, so is pi-x.
  • #1
DanielJackins
40
0

Homework Statement



Suppose that x=7pi/23 is a solution of the equation sinx= A where A is some constant.
Then A must be equal to [blank], and the other solution of the equation in the interval [0,2pi] must be x = [blank].

The Attempt at a Solution



So I've plugged the value into my calculator and found A, but I completely forget Trigonometry. How would I go about finding the second solution?

Thanks
 
Physics news on Phys.org
  • #2
The identity you need to use is sinx = sin([itex]\pi[/itex] - x). Can you see how this shows the symmetry of sinx in the first and second quadrant where two x values give the same A value?
 
  • #3
Not really, I can see it in my calculator but I don't completely understand it :P and should I be getting a different value?
 
  • #4
As Bohrok pointed out when x is a solution so too is pi-x
 

FAQ: Find the Second Solution for sinx = A | Trigonometry Question

How do you find the second solution for sinx = A?

To find the second solution for sinx = A, you need to use the inverse sine function or arcsine function. This function is denoted as sin^-1 or arcsin and it helps find the angle whose sine value is equal to A. You can use a scientific calculator or reference tables to find the inverse sine of A.

What is the significance of finding the second solution for sinx = A?

Finding the second solution for sinx = A is important because it provides a complete set of solutions for the given equation. In trigonometric equations, there can be multiple solutions for a given value, and finding the second solution helps us understand the complete behavior of the function.

How do you determine which solution is the second solution for sinx = A?

The second solution for sinx = A is usually determined by adding or subtracting 180 degrees (or π radians) from the first solution. This is because the sine function is a periodic function with a period of 360 degrees (or 2π radians), meaning that the graph repeats itself after every 360 degrees. Therefore, the second solution would be the first solution plus or minus 180 degrees.

Can there be more than two solutions for sinx = A?

Yes, there can be more than two solutions for sinx = A. This is because the sine function is a periodic function with an infinite number of solutions. In general, there can be n solutions for sinx = A, where n is any integer.

Are there any other methods for finding the second solution for sinx = A?

Yes, there are other methods for finding the second solution for sinx = A. One method is to use the unit circle and its properties to determine the angle whose sine value is equal to A. Another method is to use the double angle formula for sine, which states that sin2x = 2sinxcosx. By using this formula, you can find the second solution by solving for x.

Similar threads

What is the solution to finding d(x) without using trigonometry?
Replies
2
Views
2K
Solve Trigonometry Problem: Cos^3x+1/Cos^3x=0
Replies
24
Views
3K
Find Value of Limit Involving Trig. Identity w/o L'hopital Rule
Replies
8
Views
2K
Find the value of trigonometry
Replies
6
Views
3K
Finding points of intersection algebraically between 2 trig functions
Replies
11
Views
34K
Trigonometric Problem: Solving for sin(x/2)*cos(5p/4) with Given Conditions
Replies
18
Views
2K
Exact Value of Sin 65 Degrees: Trigonometry Identities for Finding the Solution
Replies
3
Views
5K
Trigonometry solutions Question
Replies
5
Views
2K
Resolving angle of parallelogram in 3D space
Replies
1
Views
2K
Trigonometry - Double Angle Identities
Replies
18
Views
2K

Hot Threads

Recent Insights

Back
Top