Question

Cos 60 = 1/2 and sin 60 = (sqrt3)/2. True or false

Answer 1

These statements are true.

Explanation:

In a right triangle with an angle of 60 degrees, the side opposite the 60 degree angle is half the length of the hypotenuse, and the side adjacent to the 60 degree angle is (sqrt3)/2 times the length of the hypotenuse. Therefore, we have:

cos 60 = adjacent / hypotenuse = (sqrt3)/2 / 1 = (sqrt3)/2

sin 60 = opposite / hypotenuse = 1/2 / 1 = 1/2

Hence, cos 60 = (sqrt3)/2 and sin 60 = 1/2, which confirms that the given statements are true.

Answer 2

True.

Explanation:

In a unit circle, the cosine of an angle measures the x-coordinate of the point on the unit circle that corresponds to that angle, and the sine of an angle measures the y-coordinate of the point on the unit circle that corresponds to that angle. For an angle of 60 degrees, the corresponding point on the unit circle has coordinates (1/2, √3/2). Therefore, cos 60 = 1/2 and sin 60 = √3/2. These values are true.