The expression cos 60° is equivalent to sin ?
cos 60 = 1/2 sin 60
To find the value of sin x when cos 60° is given, we can use the relationship between sine and cosine for complementary angles.
For any angle x, the sine and cosine functions satisfy the following relationship:
sin^2(x) + cos^2(x) = 1.
Since 60° and 30° are complementary angles (their sum is 90°), the value of sin 30° can be used to determine the value of sin 60°.
We know that sin 30° is equal to 1/2. Therefore, we can use the relationship mentioned earlier to find sin 60°:
sin^2(60°) + cos^2(60°) = 1.
Let's solve for sin 60°:
(1/2)^2 + cos^2(60°) = 1
1/4 + cos^2(60°) = 1
cos^2(60°) = 1 - 1/4
cos^2(60°) = 3/4
Now, to find cos 60°, we can take the square root of both sides:
cos(60°) = √(3/4)
cos(60°) = √3/2
Therefore, the expression cos 60° is equivalent to sin 30°, which is equal to √3/2.