Question

Sin(-2383)-sin(2023)+cos(-485)-cos(-125)

Answer 1

Решение прикреплено.

Использовались формулы приведения:
$sin(360+x)=sinx$
$sin(360-x)=-sinx$
$cos(360+x)=cosx$
$cos(360-x)=cosx$

Ответ:  2*sin137

Answer 2

To calculate the value of the expression sin(-2383) - sin(2023) + cos(-485) - cos(-125), you can use trigonometric identities and a calculator.

First, let's evaluate each term separately:

1. sin(-2383): Since the sine function has a period of 360 degrees (or 2π radians), you can subtract multiple full rotations from the angle to get an equivalent angle within one period. So, -2383 degrees is equivalent to -2383 degrees - 6 * 360 degrees = -223 degrees. Converting this to radians: -223 degrees * (π/180) ≈ -3.89 radians. So, sin(-2383) ≈ sin(-3.89).

2. sin(2023): Similarly, 2023 degrees is equivalent to 2023 degrees - 5 * 360 degrees = 143 degrees. Converting this to radians: 143 degrees * (π/180) ≈ 2.50 radians. So, sin(2023) ≈ sin(2.50).

3. cos(-485): Using the same logic as before, -485 degrees is equivalent to -485 degrees - 2 * 360 degrees = -485 degrees. Converting this to radians: -485 degrees * (π/180) ≈ -8.46 radians. So, cos(-485) ≈ cos(-8.46).

4. cos(-125): Again, -125 degrees is equivalent to -125 degrees - 1 * 360 degrees = -125 degrees. Converting this to radians: -125 degrees * (π/180) ≈ -2.18 radians. So, cos(-125) ≈ cos(-2.18).

Now, you can calculate these approximate values and then sum them up:

sin(-3.89) - sin(2.50) + cos(-8.46) - cos(-2.18)

Using a calculator:

sin(-3.89) ≈ -0.0705 sin(2.50) ≈ 0.5985 cos(-8.46) ≈ 0.5306 cos(-2.18) ≈ 0.7485

Now, add or subtract these values:

-0.0705 - 0.5985 + 0.5306 - 0.7485 ≈ -0.7869

So, sin(-2383) - sin(2023) + cos(-485) - cos(-125) ≈ -0.7869.