Question

Решить. 5/(4-3cos(7п/8)) С объяснением, пожалуйста.

Answer 1

To solve the expression 5/(4-3cos(7π/8)), we can follow these steps:

1. Evaluate the expression inside the cosine function: cos(7π/8). - The cosine function is a trigonometric function that calculates the ratio of the adjacent side to the hypotenuse in a right triangle. - In this case, we have cos(7π/8), which means we need to find the cosine of an angle of 7π/8 radians. - To evaluate this, we can use a calculator or refer to trigonometric tables. - The cosine of 7π/8 is approximately -0.9238795325.

2. Substitute the value of cos(7π/8) back into the original expression: 5/(4-3cos(7π/8)). - Now that we know the value of cos(7π/8) is approximately -0.9238795325, we can substitute it into the expression. - The expression becomes 5/(4-3*(-0.9238795325)).

3. Simplify the expression further. - Multiply -3 by -0.9238795325: -3*(-0.9238795325) = 2.7716385975. - The expression becomes 5/(4 + 2.7716385975).

4. Continue simplifying the expression. - Add 4 and 2.7716385975: 4 + 2.7716385975 = 6.7716385975. - The expression becomes 5/6.7716385975.

5. Calculate the final result. - Divide 5 by 6.7716385975: 5/6.7716385975 ≈ 0.7384602621.

Therefore, the solution to the expression 5/(4-3cos(7π/8)) is approximately 0.7384602621.

Please note that the values used in this explanation are approximations and may vary depending on the level of precision required.