Question

Cos270-cos150+tg315+sin(-960)

Answer 1

Ответ:

Применяем формулы приведения и используем известные значения тигонометрических функций некоторых углов , а также нечётность функции у=sinx и периодичность этой функции , Т=2π .

$cos270^\circ -cos150^\circ +tg135^\circ +sin(-960^\circ )=\\\\=0-cos(180^\circ -30^\circ )+tg(180^\circ -45^\circ )-sin(2\cdot 360^\circ +240^\circ )=\\\\=-(-cos30^\circ )-tg45^\circ -sin240^\circ =\\\\=-cos30^\circ -tg45^\circ -sin(180^\circ +60^\circ )=\\\\=cos30^\circ -tg45^\circ +sin60^\circ =\dfrac{\sqrt3}{2}-1+\dfrac{\sqrt3}{2}=\bf \sqrt3-1$

Answer 2

To evaluate the expression, let's break it down step by step:

1. cos(270): The cosine of 270 degrees is equal to 0.

2. cos(150): The cosine of 150 degrees is equal to -0.86602540378 (approximately).

3. tg(315): The tangent of 315 degrees is equal to -1 (approximately).

4. sin(-960): The sine of -960 degrees is equal to -0.34202014332 (approximately).

Now, let's substitute these values back into the original expression:

0 - (-0.86602540378) + (-1) + (-0.34202014332)

Simplifying further:

0 + 0.86602540378 - 1 - 0.34202014332

= 0.52400526046

So, the value of the expression cos(270) - cos(150) + tg(315) + sin(-960) is approximately 0.524.