Question

Sin(-2π/3)>0; cos(-3π/4)>0; tag(-π/6)>0; ctg4π/9>0

Answer 1

мы просто вычисляем значение используя таблицу значений тригонометрических функций


sin(150°)-cos(720°)+tan(225°)=1/2-1+1=1/2=0,

Answer 2

Let's evaluate each of the trigonometric expressions you provided:

1. sin(-2π/3): The sine function is an odd function, which means that sin(-x) = -sin(x) for any angle x. Therefore, we have sin(-2π/3) = -sin(2π/3). The value of sin(2π/3) is √3/2, so sin(-2π/3) = -√3/2 < 0.

2. cos(-3π/4): The cosine function is an even function, which means that cos(-x) = cos(x) for any angle x. Therefore, we have cos(-3π/4) = cos(3π/4). The value of cos(3π/4) is -√2/2, so cos(-3π/4) = -√2/2 < 0.

3. tan(-π/6): The tangent function is an odd function, so tan(-x) = -tan(x) for any angle x. Therefore, we have tan(-π/6) = -tan(π/6). The value of tan(π/6) is 1/√3, so tan(-π/6) = -1/√3 < 0.

4. cot(4π/9): The cotangent function is the reciprocal of the tangent function, so cot(x) = 1/tan(x) for any angle x. Therefore, we have cot(4π/9) = 1/tan(4π/9). The value of tan(4π/9) is √3, so cot(4π/9) = 1/√3 > 0.

In summary:

• sin(-2π/3) < 0
• cos(-3π/4) < 0
• tan(-π/6) < 0
• cot(4π/9) > 0