How Do You Solve 5sin(a+30)=3 for Values of a?

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Homework Help Overview

The problem involves solving the equation 5sin(a+30) = 3 for values of a within the interval 0 <= a <= 360 degrees. Participants are attempting to find the angle a to one decimal place.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the initial steps of isolating the sine function and using the arcsine function. There are questions about the next steps after finding the arcsine value, including whether to subtract 30 from both sides of the equation.

Discussion Status

Some participants have provided guidance on checking the calculated values against the original equation, suggesting a verification step. Multiple interpretations of the next steps are being explored, but there is no explicit consensus on the final answers yet.

Contextual Notes

Participants express uncertainty about the method and are revisiting fundamental concepts related to solving trigonometric equations. The discussion reflects a collaborative effort to clarify the approach without providing complete solutions.

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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
 
Last edited:
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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

How about subtracting 30 from both sides?
 
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

What do you get if you subtract 30 from both sides?
 
a = 6.8...
so

a = 6.8, 180 - 6.869..,
a = 6.8 and 173.1...
is that my final answer?
 
Looks good, how about checking those numbers back in the original equation? Then you can be sure.

I.e., does 5sin(6.869+30) equal 3? And similarly for 173.131
 

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