Question

What is the exact value of sin(264°)cos(6°) cos(264°)sin(6°)?

1) –1
2) negative one-half
3) 0
4) 1

Answer 1

The exact value of sin(264°)cos(6°) cos(264°)sin(6°) is approximately -0.7192

Step-by-step explanation:

To find the exact value of sin(264°)cos(6°) cos(264°)sin(6°), we can use the trigonometric identity sin(a)cos(b) = (1/2)[sin(a+b) + sin(a-b)]. So, sin(264°)cos(6°) cos(264°)sin(6°) = (1/2)[sin(270°) + sin(258°)].

Now, sin(270°) = -1 and sin(258°) = -0.4384. Therefore, (1/2)[sin(270°) + sin(258°)] = (1/2)(-1 - 0.4384) = -0.7192.

Hence, the exact value of sin(264°)cos(6°) cos(264°)sin(6°) is approximately -0.7192.