Question

Cos(-570)+√3sin(-300)+2tg(-135)

Answer 1

\begin{lgathered}cos(-570)+ \sqrt{3}sin(-300)+2tg(-135)= \\\ =cos(2\cdot360-570)+ \sqrt{3}sin(360-300)+2tg(180-135)= \\\ =cos150+ \sqrt{3}sin60+2tg45=- \frac{\sqrt{3}}{2} +\sqrt{3}\cdot\frac{\sqrt{3}}{2}+2\cdot1= \\\ =- \frac{\sqrt{3}}{2} +\frac{3}{2}+2=3.5- \frac{\sqrt{3}}{2}\end{lgathered}​cos(−570)+√​3​​​sin(−300)+2tg(−135)=​ =cos(2⋅360−570)+√​3​​​sin(360−300)+2tg(180−135)=​ =cos150+√​3​​​sin60+2tg45=−​2​​√​3​​​​​+√​3​​​⋅​2​​√​3​​​​​+2⋅1=​ =−​2​​√​3​​​​​+​2​​3​​+2=3.5−​2​​√​3​​​​​​​

Answer 2

Вот, держи! Ответик :3

Answer 3

To calculate the value of the expression, we first need to convert the trigonometric functions from degrees to radians. Remember the following conversions:

• Degrees to Radians: π radians = 180 degrees
• Radians to Degrees: 180 degrees = π radians

Now, let's calculate each term step by step:

1. Cosine of -570 degrees: We know that cos(-θ) = cos(θ), so cos(-570) = cos(570).

To convert 570 degrees to radians, we divide by 180 and multiply by π: 570 degrees * (π radians / 180 degrees) = 57π/18 radians = 19π/6 radians.

Now, we calculate the cosine of 19π/6 radians: cos(19π/6) = cos(π + π/6) = -cos(π/6) = -√3/2.

2. Square root of 3 times sine of -300 degrees: We know that sin(-θ) = -sin(θ), so sin(-300) = -sin(300).

To convert 300 degrees to radians, we divide by 180 and multiply by π: 300 degrees * (π radians / 180 degrees) = 5π/3 radians.

Now, we calculate the sine of 5π/3 radians: sin(5π/3) = sin(π + 2π/3) = sin(2π/3) = √3/2.

Multiply √3 by √3/2: √3 * √3/2 = 3/2.

3. Tangent of -135 degrees: We know that tan(-θ) = -tan(θ), so tan(-135) = -tan(135).

To convert 135 degrees to radians, we divide by 180 and multiply by π: 135 degrees * (π radians / 180 degrees) = 3π/4 radians.

Now, we calculate the tangent of 3π/4 radians: tan(3π/4) = -1.

Now, let's put all the calculated values together in the original expression:

Cos(-570) + √3sin(-300) + 2tg(-135) = -√3/2 + 3/2 - 2 = -√3/2 + 1/2 = (1 - √3)/2.

So, the final value of the expression is (1 - √3)/2.