Solve for Theta in bsin30-85.7sin(theta)=0

So on a calculator, you would enter sin^-1(b*sin(30)/85.7) to find theta. In summary, to make theta the subject, solve for sin(theta) by using the inverse function arcsin. This can be done by plugging in the values for b and 30 degrees into the equation sin(theta)=-bsin30/-85.7 and using the arcsin function on a calculator.
  • #1
Ry122
565
2
in bsin30-85.7sin(theta)=0
How can I make theta the subject?
 
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  • #2
Solve for sin(theta) and use arcsin.
 
  • #3
how is that done?
 
  • #4
Ry122 said:
how is that done?
It's the inverse.

Recall ...

[tex]y=x^2,x\geq0[/tex]

[tex]f^{-1}(x)=\sqrt x[/tex]

So similarly ...

[tex]\sin x=y[/tex]

[tex]\sin^{-1}y=x[/tex]
 
  • #5
so is this correct
sin(theta)=-bsin30/-85.7
1/sin(theta)=(-85.7)/(-binsin30)sin^-1(-bsin30/-85.7)=(theta)
 
Last edited:
  • #6
That doesn't make it the subject, now does it? If sin(theta)=a, then theta=arcsin(a). That's the definition of arcsin.
 
  • #7
I forgot to add that arcsine is defined in Quadrants I & IV. It's domain is: [tex]-\frac{\pi}{2}\leq y\leq\frac{\pi}{2}[/tex].
 
  • #8
Ry122 said:
so is this correct
sin(theta)=-bsin30/-85.7
1/sin(theta)=(-85.7)/(-binsin30)


sin^-1(-bsin30/-85.7)=(theta)
I think what you did was implied something like ... [tex]\frac{1}{x}=x^{-1}[/tex]

It's not the same, the reciprocal of sine is cosecant. Refer to Dick's post.
 
  • #9
Ry122 said:
so is this correct
sin(theta)=-bsin30/-85.7
1/sin(theta)=(-85.7)/(-binsin30)


sin^-1(-bsin30/-85.7)=(theta)

Yes. That's it. arcsin(b*sin(30)/85.7)=theta.
 
  • #10
That's it. arcsin(b*sin(30)/85.7)=theta.
How do you work this out on a calculator?
 
  • #11
To work it out on a calculator you need to know b, right? The arcsin function is usually labeled sin^(-1).
 

1. What is the equation "bsin30-85.7sin(theta)=0" used for?

The equation "bsin30-85.7sin(theta)=0" is used to solve for the value of theta, which is an angle in a right triangle, given the value of b and other trigonometric functions.

2. How do I solve for theta in this equation?

To solve for theta, you can use the trigonometric identity sin(a-b)=sin(a)cos(b)-cos(a)sin(b) to rewrite the equation as bsin(30)-85.7sin(theta)=0. Then, you can use the inverse sine function to isolate theta and solve for its value.

3. What does b stand for in this equation?

The variable b represents the length of the side opposite to the angle theta in a right triangle.

4. Can this equation be solved without a calculator?

Yes, this equation can be solved without a calculator by using trigonometric identities and solving for theta algebraically.

5. What is the range of possible values for theta in this equation?

The range of possible values for theta in this equation is from 0 to 180 degrees or 0 to π radians, as these are the possible values for an angle in a right triangle.

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