1) sin x < 1/4 2) sin x > - 1/4 3) cos x > 1/3

Предыдущий
вопрос Следующий
вопрос

To solve these inequalities, we need to consider the unit circle and the values of sine and cosine for different angles.

1) sin x < 1/4
Looking at the unit circle, we see that the maximum value of sine is 1 and the minimum value is -1. Therefore, for sin x to be less than 1/4, x must be within the range where sin x is positive and less than 1/4. This occurs in the first and second quadrants. So, x ∈ (arcsin(1/4), π - arcsin(1/4)) + 2πk, where k is an integer.

2) sin x > -1/4
For sin x to be greater than -1/4, x must be within the range where sin x is negative and greater than -1/4. This occurs in the third and fourth quadrants. So, x ∈ (-π + arcsin(1/4), -arcsin(1/4)) + 2πk, where k is an integer.

3) cos x > 1/3
Looking at the unit circle, we see that the maximum value of cosine is 1 and the minimum value is -1. Therefore, for cos x to be greater than 1/3, x must be within the range where cos x is positive and greater than 1/3. This occurs in the first and fourth quadrants. So, x ∈ (arccos(1/3), 2π - arccos(1/3)) + 2πk, where k is an integer.