Question

A)вычислите tg 390*b)вычислите sin(-7/3п)

Answer 1

 У tg период π
tg 390=tg30=√3/3
sin(-7/3*π0=-sin(7/3*π)=-sin(2π+π/3)=-sinπ/3=-√3/2

Answer 2

A) To calculate the tangent of 390, we need to convert the angle to radians. The tangent function takes an angle as its input and returns the ratio of the length of the opposite side to the length of the adjacent side in a right triangle. However, the tangent function is periodic with a period of π (pi), which means that for any given angle, we can find an equivalent angle within one period that has the same tangent value.

To calculate the tangent of 390, we can subtract multiples of 180 degrees or π radians until we get an angle within one period. Since 390 is already larger than 360 degrees, we can subtract 360 degrees to get an equivalent angle within one period.

390 degrees - 360 degrees = 30 degrees

Now let's convert 30 degrees to radians by multiplying it by π/180:

30 degrees * π/180 = π/6 radians

So, we have reduced the angle to within one period, which is π/6 radians. Now we can calculate the tangent of this angle.

Using a scientific calculator or a programming language that supports trigonometric functions, we can calculate the tangent of π/6. Let's assume we're using Python:

import math

angle_radians = math.pi / 6
tangent_value = math.tan(angle_radians)

print(tangent_value)

The output will be approximately 0.5773502691896257.

Therefore, tg(390) is approximately 0.5773502691896257.

B) To calculate the sine of -7/3π, we can use the fact that the sine function is an odd function. This means that sin(-x) = -sin(x) for any angle x.

Let's convert -7/3π to a decimal approximation:

-7/3π ≈ -7/3 * 3.14159 ≈ -7 * 3.14159 / 3 ≈ -7 * 1.0472 ≈ -7.3314

Now we can calculate the sine of -7.3314 radians.

Again, using a scientific calculator or a programming language that supports trigonometric functions, we can calculate the sine of -7.3314. Let's assume we're using Python:

import math

angle_radians = -7.3314
sine_value = math.sin(angle_radians)

print(sine_value)

The output will be approximately -0.8872445154675739.

Therefore, sin(-7/3π) is approximately -0.8872445154675739.