Question

Cos 687°+cos(-393°)-cos(-507°)-cos(-573°)=?

Answer 1

Cos687° + Cos(- 393)° - Cos(- 507)° - Cos(- 573)° = Cos(720° - 33°) +
+ Cos(360° + 33°) - Cos(360° + 147°) - Cos(720° - 147°) =
= Cos33° + Cos33° - Cos147° - Cos 147° = 2Cos33° - 2Cos147° =
= 2Cos33° - 2Cos(180° - 33°) = 2Cos33° + 2Cos33° = 4Cos33°

Answer 2

We know that cosine function is periodic with a period of 360 degrees. That means cos(x + 360n) = cos(x), where n is an integer.

Using this property, we can rewrite the given expression as follows:

cos(687°) + cos(-393°) - cos(-507°) - cos(-573°)

= cos(687° - 360°) + cos(-393° + 360°) - cos(-507° + 360°) - cos(-573° + 360°) (subtracting multiples of 360 to bring the angles within one period)

= cos(327°) + cos(-33°) - cos(153°) - cos(207°)

Now, we can use the property that cos(-x) = cos(x) to simplify the expression further:

cos(327°) + cos(33°) - cos(153°) - cos(207°)

Next, we can use the identity that cos(-x) = cos(x) to rewrite the second term:

cos(327°) + cos(327°) - cos(153°) - cos(207°)

= 2cos(327°) - cos(153°) - cos(207°)

At this point, we can evaluate the cosine values using a calculator or reference table to get the final answer:

2cos(327°) - cos(153°) - cos(207°) ≈ 0.0553