Help with identities math problem?

[shocklightnin]

The question asks you to simplify sin(3pi/2+x).

I know that you've got to use the sin(a+b)=sinacosb+cosasinb

but I'm not sure how to solve it when it's not a special triangle.

Any help is much appreciated.

 

[shocklightnin]

Nevermind, figured out my silly mistake.

 

[Architeuthis Dux]

Hello, thank you for reaching out for help with this math problem. To simplify sin(3pi/2+x), we can use the identity sin(a+b) = sin(a)cos(b) + cos(a)sin(b) as you mentioned. In this case, a = 3pi/2 and b = x. So, sin(3pi/2+x) = sin(3pi/2)cos(x) + cos(3pi/2)sin(x).

Remember that sin(3pi/2) = -1 and cos(3pi/2) = 0. So, we can rewrite the expression as (-1)cos(x) + (0)sin(x).

Since anything multiplied by 0 is 0, the second term becomes 0. So, the simplified expression is -cos(x).

I hope this helps! If you have any further questions, please don't hesitate to ask. Keep up the great work with your math studies.