Question

1) 2 sin 150⁰- 4 cos 120⁰ 2) sin 90⁰(tg 150⁰ cos 135⁰ - the 120⁰ cos 135⁰)²помогите пж!!!!! 9класс геометрия ​

Answer 1

Ответ:

1) Sin150= (180-150)=sin30=1/2

cos120=(180-120)=-cos60=-1/2

1/2*2-4*1/2=3

2) sin150=(180-120)=sin60=корень3/2

Cos150=(180-150)=cos30=корень3/2

tg135=-1

Корень3/2*2*4*корень3/2*-1=-6

Answer 2

1) Let's solve the expression 2 sin 150° - 4 cos 120°:

To solve this expression, we need to know the values of sin 150° and cos 120°.

According to the unit circle, sin 150° is equal to 0.5 and cos 120° is equal to -0.5.

Now we can substitute these values into the expression:

2 sin 150° - 4 cos 120° = 2 * 0.5 - 4 * (-0.5) = 1 - (-2) = 1 + 2 = 3.

Therefore, the value of the expression 2 sin 150° - 4 cos 120° is 3.

2) Let's solve the expression sin 90° (tg 150° + cos 135° - the 120° cos 135°)²:

To solve this expression, we need to know the values of sin 90°, tg 150°, cos 135°, and cos 120°.

According to the unit circle, sin 90° is equal to 1, cos 135° is equal to -√2/2, and cos 120° is equal to -0.5.

Now let's calculate tg 150°. We know that tg 150° is equal to sin 150° / cos 150°. According to the unit circle, sin 150° is equal to 0.5 and cos 150° is equal to √3/2. Therefore, tg 150° = 0.5 / (√3/2) = 1 / √3 = √3 / 3.

Now we can substitute these values into the expression:

sin 90° (tg 150° + cos 135° - the 120° cos 135°)² = 1 * (√3 / 3 + (-√2/2) - (-0.5))² = (√3 / 3 - √2/2 + 0.5)².

To simplify this expression, we can use the fact that (a - b + c)² = a² - 2ab + b² + 2ac - 2bc + c²:

(√3 / 3 - √2/2 + 0.5)² = (√3 / 3)² - 2 * (√3 / 3) * (√2/2) + (√2/2)² + 2 * (√3 / 3) * 0.5 - 2 * (√2/2) * 0.5 + 0.5².

Simplifying further:

(√3 / 3)² = 3/9 = 1/3, (√2/2)² = 2/4 = 1/2, 0.5² = 0.25.

Substituting these values back into the expression:

(√3 / 3 - √2/2 + 0.5)² = (1/3) - 2 * (√3 / 3) * (√2/2) + (1/2) + 2 * (√3 / 3) * 0.5 - 2 * (√2/2) * 0.5 + 0.25.

Now we can simplify this expression further:

(1/3) - 2 * (√3 / 3) * (√2/2) + (1/2) + 2 * (√3 / 3) * 0.5 - 2 * (√2/2) * 0.5 + 0.25 = 1/3 - √6/3 + 1/2 + √3/3 - 1 + 0.25.

Combining like terms:

1/3 - √6/3 + 1/2 + √3/3 - 1 + 0.25 = (1/3 + 1/2 + √3/3) - (√6/3 - 1 + 0.25) = (2/6 + 3/6 + √3/3) - (√6/3 - 0.75).

Simplifying further:

(2/6 + 3/6 + √3/3) - (√6/3 - 0.75) = (5/6 + √3/3) - (√6/3 - 0.75).

Now we can combine the terms:

(5/6 + √3/3) - (√6/3 - 0.75) = 5/6 + √3/3 - √6/3 + 0.75.

Therefore, the value of the expression sin 90° (tg 150° + cos 135° - the 120° cos 135°)² is 5/6 + √3/3 - √6/3 + 0.75.

Please note that the above calculations are based on the given values and mathematical principles.