Question

Найдите значения выражений 1)cos7П\6 2) cos 4п\3

Answer 1

Если тебе сложно, когда присутствует π, переводи в градусы
7π/6 = 210°, а 4π/3 = 240
получается: cos210=cos(270-210)=sin60 (проверяем знак в четверти) = знак будет минус, так как 3 четверть, поэтому ответ = -√3/2
                     сos240=cos(270-240)=sin30 (проверяем знак) = знак минус, так как 3 четверть, поэтому ответ = -1/2

Answer 2

1) cos(7π/6): To find the value of cos(7π/6), we can first determine the reference angle, which is π/6. The reference angle is the acute angle formed between the terminal side of the angle and the x-axis.

Since 7π/6 is in the third quadrant, the cosine function is negative in this quadrant. Therefore, the value of cos(7π/6) is the same as the cosine of the reference angle, but with a negative sign.

cos(7π/6) = -cos(π/6)

Now, we can find the value of cos(π/6) using the unit circle or trigonometric identities. The cosine of π/6 is √3/2.

Therefore, cos(7π/6) = -√3/2.

2) cos(4π/3): To find the value of cos(4π/3), we can again determine the reference angle, which is π/3. The reference angle is the acute angle formed between the terminal side of the angle and the x-axis.

Since 4π/3 is in the third quadrant, the cosine function is negative in this quadrant. Therefore, the value of cos(4π/3) is the same as the cosine of the reference angle, but with a negative sign.

cos(4π/3) = -cos(π/3)

Now, we can find the value of cos(π/3) using the unit circle or trigonometric identities. The cosine of π/3 is 1/2.

Therefore, cos(4π/3) = -1/2.

In summary: 1) cos(7π/6) = -√3/2 2) cos(4π/3) = -1/2