Find the exact value of each expression:
1) $\sin{(-\frac{\pi}{2} +\frac{\pi}{3})}$
-For this question, it would appear as though you could use the addition compound angle formula $\sin{(A+B)}=\sin{A}\cos{B}+\sin{B}\cos{A}$, however due to the $-$ sign in front of the $\frac{\pi}{2}$, I am not sure if this is still considered to be apart of the special triangles. I know that $\frac{\pi}{2}$ (90 degrees) is. By the way, these questions are to be in radian measure.
2) $\tan{ (\frac{7\pi}{12})}$
-I think this one can be split into $\tan{(\frac{3\pi}{12} + \frac{4\pi}{12})}$ and get $\tan{(\frac{\pi}{4} + \frac{\pi}{3})}$ and then input the values into $\tan{(A+B)}=\frac{\tan{A}+\tan{B}}{1-\tan{A}\tan{B}}$
3) $2\sin{\frac{\pi}{8}}\cos{\frac{\pi}{8}}$
-This one I am not sure about where to begin. I am not sure which identity I would use here since this could be $\sin{a}\cos{b}$ could be used with either addition or subtraction.
If someone could help me out with these questions, that would be great!
Best Answer
HINT:
Recount $\sin(A+B)$ formula holds true for all finite values of $A,B$
$(1)$ How about $A=-\dfrac\pi2, B=\dfrac\pi3$
$(2)$ Proceed with the formula
$(3)$ Put $A=B$ in $\sin(A+B)$ formula