Question

Sin360° - sin(-390)/tg(-765°)

Answer 1

$sin0 - \frac{sin30}{tg45} = 0+0.5= 0.5$

Answer 2

To calculate the value of the expression:

sin(360°) - sin(-390°) / tan(-765°)

First, let's simplify each component separately:

1. sin(360°) is equal to sin(0°) because the sine function is periodic with a period of 360 degrees. So, sin(360°) = sin(0°) = 0.

2. sin(-390°) is the same as sin(390°) because the sine function is also periodic in the negative direction with a period of 360 degrees. So, sin(-390°) = sin(390°).

3. tan(-765°) is the same as tan(765°) because the tangent function is also periodic with a period of 180 degrees. So, tan(-765°) = tan(765°).

Now, let's calculate the values:

1. sin(360°) = 0

2. sin(390°) is the same as sin(30°) because 390° is equivalent to 30° after reducing the angle within a single period. You can find the sine of 30° by knowing that it's equal to 1/2.

   sin(30°) = 1/2

3. tan(765°) is the same as tan(225°) because 765° is equivalent to 225° after reducing the angle within a single period. You can find the tangent of 225° by knowing that it's equal to -1.

   tan(225°) = -1

Now, substitute these values back into the original expression:

0 - (1/2) / (-1)

Now, simplify further:

0 + 1/2

1/2

So, the value of the expression sin(360°) - sin(-390°) / tan(-765°) is 1/2.