Question

Sinx=-1 cosx=корень из 2\2 tgx=-корень из 3

Answer 1

Решение
1)  Sinx = - 1
x = - π/2 + 2πk, k ∈ Z
2)  cosx = √2\2
x = + - arccos(√2/2) + 2πn, n ∈ Z
x = + - π/4 + 2πn, n ∈ Z
3)  tgx = -√3
x = arctg(- √3) + πk, k ∈ Z
x = - π/3 + πk, k ∈ Z

Answer 2

To find the values of the trigonometric functions at these specific angles, we can use the unit circle and the definitions of the trigonometric functions. Let's analyze each of these equations:

1. sin(x) = -1 This means that the sine of the angle x is -1. In the unit circle, -1 corresponds to the point (0, -1). Since the sine value is the y-coordinate of the point on the unit circle, we can say that sin(x) = -1 when x = -π/2 + 2πn, where n is an integer.

2. cos(x) = √2/2 This means that the cosine of the angle x is √2/2. In the unit circle, √2/2 corresponds to the points (±√2/2, ±√2/2). Since the cosine value is the x-coordinate of the point on the unit circle, we can say that cos(x) = √2/2 when x = π/4 + 2πn or x = 7π/4 + 2πn, where n is an integer.

3. tan(x) = -√3 This means that the tangent of the angle x is -√3. In the unit circle, -√3 corresponds to the points (-√3, -1) and (√3, 1). Since the tangent value is the y-coordinate divided by the x-coordinate of the point on the unit circle, we can say that tan(x) = -√3 when x = 5π/6 + πn, where n is an integer.

In summary:

• sin(x) = -1 when x = -π/2 + 2πn, where n is an integer.
• cos(x) = √2/2 when x = π/4 + 2πn or x = 7π/4 + 2πn, where n is an integer.
• tan(x) = -√3 when x = 5π/6 + πn, where n is an integer.