thomas49th said:Homework Statement
find the values of a to 1 decimal place for the interval 0 <= a <= 360 for which
5sin (a+30) = 3
The Attempt at a Solution
I know this is really easy but I've forgotten the method :(
somthing like
(a + 30) = arcsin(3/5)
a + 30 = 36.869...
but I am not sure where to go from there.
Thanks
thomas49th said:Homework Statement
find the values of a to 1 decimal place for the interval 0 <= a <= 360 for which
5sin (a+30) = 3
The Attempt at a Solution
I know this is really easy but I've forgotten the method :(
somthing like
(a + 30) = arcsin(3/5)
a + 30 = 36.869...
but I am not sure where to go from there.
Thanks
The equation 5sin(a+30)=3 is a mathematical expression that represents the relationship between the sine of an angle (a+30) and the number 3. It is asking to solve for the value of a that makes the equation true.
To solve for a, you will need to use algebraic manipulation and trigonometric identities. First, isolate the sine term by dividing both sides by 5. Then, use the inverse sine function to find the value of (a+30). Finally, subtract 30 from both sides to find the value of a.
Yes, you can use a calculator to solve this equation. However, make sure your calculator is set to the correct mode (degrees or radians) and that you are using the inverse sine function to find the value of (a+30).
Yes, there are multiple solutions for a in this equation. This is because the sine function has a periodic nature and can have multiple angles that produce the same value. You will need to use the general solution, which involves adding or subtracting integer multiples of 360 degrees or 2π radians to the initial value of (a+30).
You can check your solution by substituting the value of a into the original equation and seeing if it produces the number 3. You can also graph the equation and see if the resulting point lies on the curve.