Question

Cos(-225⁰)+sin675⁰+tg(-1035⁰)​

Answer 1

Ответ:

1-√2

Объяснение:

cos(-225⁰)+sin675⁰+tg(-1035⁰) = cos225⁰ +sin675⁰-tg1035⁰ =

= cos(180⁰+45⁰) + sin(630⁰+45⁰) - tg(1080⁰-45⁰) =

= -cos 45⁰ +sin(90⁰*7 +45⁰) - tg(180⁰*6-45⁰) =

= - √2/2 + (- sin45⁰) - (-tg45⁰) =

=   - √2/2 -  √2/2 - (-1) = -√2 + 1 = 1-√2

Для решения использованы свойства чётности и нечетности тригонометрических функций и формулы приведения.

Answer 2

To calculate the value of the expression:

cos(-225°) + sin(675°) + tan(-1035°)

we need to use the trigonometric identities and convert the angles to their equivalent angles within the range of 0° to 360°.

Let's evaluate each term separately:

1. cos(-225°): The cosine function has a period of 360°, so we can add or subtract multiples of 360° without changing the value. We can convert -225° to an equivalent angle within the range of 0° to 360°:

-225° + 360° = 135°

The cosine of 135° is equal to the cosine of its reference angle (180° - 135° = 45°), which is 1/√2 or approximately 0.7071.

2. sin(675°): Similar to the cosine function, the sine function has a period of 360°. We can find an equivalent angle within the range of 0° to 360°:

675° - 2 × 360° = -45°

The sine of -45° is equal to the negative sine of its reference angle (45°), which is -1/√2 or approximately -0.7071.

3. tan(-1035°): The tangent function has a period of 180°, so we can add or subtract multiples of 180° without changing the value. We can find an equivalent angle within the range of -180° to 0°:

-1035° + 2 × 180° = -675°

The tangent of -675° is equal to the tangent of its reference angle (-675° + 180° = -495°), which is 1 or approximately 1.

Now, let's substitute the values back into the original expression and calculate the result:

cos(-225°) + sin(675°) + tan(-1035°) = 0.7071 + (-0.7071) + 1 = 1.7071

Therefore, the value of the expression cos(-225°) + sin(675°) + tan(-1035°) is approximately 1.7071.