How can I simplify sin(x + (pi/6))?

[ELIZAeffect]

OK, I worked through an assignment wanting me to rewrite formulas. However two problems are driving me crazy.

sin(x + (pi/6))
I get (sqrt(3)/2)sinX + (1/2)cosX
not really too simplified.

(sin^2(2x))(cos^2(2x))
((1-cos4x)/2) ((1+cos4x)/2)
(1-cos^2(4x))(1/4)
[((2/2)-((1+cos8x)/2)](1/4)
((1+cos8x)/4)(1/4)
(1 + cos8x)(1/16)
//When I plug numbers in I do not get a valid solution for the original equation so I messed up somewhere.

Any guidance is appreciated. Thank you for your time and knowledge. Also, congratulations this site has grown a lot since my old days of getting on about everyday. Job got in the way and all.

 

[dextercioby]

The first one cannot be simplified indeed...

The second is
$$\sin^{2}2x\cos^{2}2x$$

,or i didn't understant it??

HINT:
Use
$$\sin 2u=2\sin u\cos u$$

Daniel.

 

[wais]

To simplify sin(x + (pi/6)), you can use the trigonometric identity sin(a+b) = sin(a)cos(b) + cos(a)sin(b). In this case, a = x and b = (pi/6). Therefore, sin(x + (pi/6)) = sin(x)cos(pi/6) + cos(x)sin(pi/6). Since cos(pi/6) = sqrt(3)/2 and sin(pi/6) = 1/2, the simplified form would be (sqrt(3)/2)sin(x) + (1/2)cos(x).

For the second problem, you have correctly simplified it to (1+cos8x)/16. However, when plugging in numbers, make sure you are using radians instead of degrees. Also, check your calculations to see if you have made any mistakes.

I'm glad you find this site helpful and congratulations on your job! Keep practicing and you'll improve your math skills.