4.40

It appears you have a page from a textbook with trigonometry problems. Since it's in a language I can't identify, I can't give precise solutions, but I can guide you in understanding the trigonometric functions and concepts that may be involved. Here's a general overview of the trigonometric functions:

1. Sine (sin): It represents the ratio of the length of the side opposite the angle to the hypotenuse of a right triangle.

2. Cosine (cos): It represents the ratio of the length of the adjacent side to the hypotenuse.

3. Tangent (tan): It is the ratio of the sine to the cosine, or the opposite side to the adjacent side.

4. Cotangent (cot), Secant (sec), and Cosecant (csc): These are the reciprocals of tangent, cosine, and sine, respectively.

For problem-solving in trigonometry:

• Use identities like Pythagorean identity: \( \sin^2 \theta + \cos^2 \theta = 1 \).

• Angle sum and difference identities can be helpful:

  • \( \sin(a \pm b) = \sin a \cos b \pm \cos a \sin b \)
  • \( \cos(a \pm b) = \cos a \cos b \mp \sin a \sin b \)

• Understand the unit circle and how angles correspond to points on the circle, which helps visualize sine and cosine values.

If you have specific questions or need a particular problem translated or solved, providing context or the specific text might be helpful.