Question

Sin(-300°)×cos(-135°)×tg(-210°)×ctg(-120°)

Answer 1

Ответ: sin(-300°)cos(-135°)tg(-210°)ctg(-120°)=(-sin(300°))cos(135°)(-tg(210°))(-ctg(120°))=-sin(360°-60°)cos(180°-45°)tg(270°-60°)ctg(180°-60°)=sin60°(-cos45°)ctg60°(-ctg60°)=sin60°cos45°ctg²60°=√3/2 × √2/2 × 1/√3 × 1/√3 = √6/4 × 1/3 = √6/12

Answer 2

To calculate the product of the trigonometric functions sin(-300°), cos(-135°), tan(-210°), and cot(-120°), we can break it down step by step:

1. sin(-300°): sin(-300°) is equivalent to sin(-300° + 360°), which is sin(60°). The sine function of 60 degrees is √3/2.

2. cos(-135°): cos(-135°) is equivalent to cos(-135° + 360°), which is cos(225°). The cosine function of 225 degrees is -√2/2.

3. tan(-210°): tan(-210°) is equivalent to tan(-210° + 360°), which is tan(150°). The tangent function of 150 degrees is -√3.

4. cot(-120°): cot(-120°) is equivalent to cot(-120° + 360°), which is cot(240°). The cotangent function of 240 degrees is -√3.

Now, multiply all these values together: (sin(60°) * cos(225°) * tan(150°) * cot(240°)) = (√3/2 * (-√2/2) * (-√3) * (-√3)) = (√3/2 * √2/2 * √3 * √3) = (√3 * √2 * √3 * √3) = (3 * 2 * 3) = 18

So, sin(-300°) * cos(-135°) * tan(-210°) * cot(-120°) equals 18.