Question

Arccos (-1/2) cos(arccos 0,6)

Answer 1

arccos (-1/2)=$\frac{2\pi }{3}$ или 120°.

cos(arccos 0,6)=0,6 или $\frac{3}{5}$

Answer 2

1) Arccos(-1/2): The arccosine function (arccos) gives us the angle whose cosine is equal to the given value. In this case, we want to find the angle whose cosine is -1/2.

The cosine function is positive in the first and fourth quadrants, so we know that the angle we are looking for is either in the first quadrant or in the fourth quadrant.

To find the angle in the first quadrant, we can use the inverse cosine function (arccos) on the absolute value of -1/2: arccos(|-1/2|) = arccos(1/2) ≈ 60 degrees or π/3 radians.

To find the angle in the fourth quadrant, we can subtract the angle in the first quadrant from 360 degrees or 2π radians: 360 - 60 = 300 degrees or 2π - π/3 = 5π/3 radians.

So, the possible angles whose cosine is -1/2 are approximately 60 degrees or π/3 radians in the first quadrant, and 300 degrees or 5π/3 radians in the fourth quadrant.

2) cos(arccos 0.6): In this case, we want to find the cosine of the angle whose arccosine is equal to 0.6.

Using the definition of arccosine, we know that arccos(0.6) is the angle whose cosine is 0.6.

So, cos(arccos 0.6) = 0.6.

Therefore, the cosine of the angle whose arccosine is 0.6 is 0.6.