What is sin (x + (pi/4)) when sin x = 1/2?

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To find sin(x + (pi/4)) when sin x = 1/2, first determine the value of x within the range of 0 to pi/2, which is x = pi/6. Using the sine addition formula, sin(a + b) = sin a cos b + cos a sin b, substitute a with pi/6 and b with pi/4. This results in sin(pi/6) = 1/2 and cos(pi/6) = √3/2, while sin(pi/4) = √2/2 and cos(pi/4) = √2/2. Therefore, sin(x + (pi/4)) simplifies to (1/2)(√2/2) + (√3/2)(√2/2), yielding the final answer of (√2 + √6)/4.
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Simple trigonometry...

Just some simple Trigonometry...

If sin x = 1/2, then what is sin (x + (pi/4)), if x is greater than or equal to 0 and less or equal to pi over 2?

Method?
 
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Start by figuring out all the values of x that satisfy sin x = 1/2 (between 0 and pi/2). (There's only one.)
 
It specifies do not use calculator or log tables...
 
I presume you are expected to know the properties of some special right triangles and special angles? (For example: a 3-4-5 right triangle)

You need some facts at your disposal to get started.
 
I'm not sure. I haven't seen a question like this one before. So basically I have to know the properties of the triangle? I can draw one with the sin = 1-2 to part...but where from there?
 

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