To simplify this expression, first we need to find the values of cos(-π/6) and sin(-π/2).
We know that cos(-π/6) = cos(π/6) because the cosine function is an even function. Since cos(π/6) = √3/2, we have cos(-π/6) = √3/2.
Similarly, sin(-π/2) = -sin(π/2) because the sine function is an odd function. Since sin(π/2) = 1, we have sin(-π/2) = -1.
Now, substituting these values into the given expression:
34√3 cos(-π/6) sin(-π/2)= 34√3 (√3/2) (-1)= -34 * 3/2= -51
Therefore, 34√3cos(-π/6)sin(-π/2) simplifies to -51.
To simplify this expression, first we need to find the values of cos(-π/6) and sin(-π/2).
We know that cos(-π/6) = cos(π/6) because the cosine function is an even function. Since cos(π/6) = √3/2, we have cos(-π/6) = √3/2.
Similarly, sin(-π/2) = -sin(π/2) because the sine function is an odd function. Since sin(π/2) = 1, we have sin(-π/2) = -1.
Now, substituting these values into the given expression:
34√3 cos(-π/6) sin(-π/2)
= 34√3 (√3/2) (-1)
= -34 * 3/2
= -51
Therefore, 34√3cos(-π/6)sin(-π/2) simplifies to -51.