Question

Sin pi/4*cos pi/4-sin pi/3*cos pi/6

Answer 1

sin(π/4)·cos(π/4) - sin(π/3)·cos(π/6) = I

$\sin(\frac{\pi}{4}) = \frac{\sqrt{2}}{2}$

$\cos(\frac{\pi}{4}) = \frac{\sqrt{2}}{2}$

$\sin(\frac{\pi}{3}) = \frac{\sqrt{3}}{2}$

$\cos(\frac{\pi}{6}) = \frac{\sqrt{3}}{2}$

$I = \frac{\sqrt{2}}{2}\cdot\frac{\sqrt{2}}{2} -$

$- \frac{\sqrt{3}}{2}\cdot\frac{\sqrt{3}}{2} =$

$= \frac{2-3}{4} = -\frac{1}{4} = -0{,}25$

Answer 2

To evaluate the expression sin(pi/4) * cos(pi/4) - sin(pi/3) * cos(pi/6), we can use the trigonometric identities to simplify it.

First, let's rewrite the angles in radians:

sin(pi/4) * cos(pi/4) - sin(pi/3) * cos(pi/6)

Using the identity sin(θ) * cos(θ) = (1/2) * sin(2θ), we can rewrite the expression as:

(1/2) * sin(2(pi/4)) - (1/2) * sin(2(pi/3))

Next, let's simplify the angles:

2(pi/4) = pi/2

2(pi/3) = (2/3)pi

Now we can substitute these values back into the expression:

(1/2) * sin(pi/2) - (1/2) * sin((2/3)pi)

The value of sin(pi/2) is 1, and sin((2/3)pi) is (√3)/2. Substituting these values, we have:

(1/2) * 1 - (1/2) * (√3)/2

Simplifying further, we get:

1/2 - (√3)/4

To rationalize the denominator, we can multiply the numerator and denominator of the second term by 2:

1/2 - (2√3)/4

Now we can combine the terms:

1/2 - (2√3)/4 = (2 - 2√3)/4

Therefore, the simplified expression is:

(2 - 2√3)/4.