which of the following expressions has the same value as cos 30°?
sin π/6
sin 30°
cos π/6
cos 60°
To determine which expression has the same value as cos 30°, let's break down each expression:
1. sin π/6: To find the value of sin π/6, we can use the trigonometric identity sin θ = cos (π/2 - θ). Here, sin π/6 = cos (π/2 - π/6) = cos (π/3). Therefore, sin π/6 does not have the same value as cos 30°.
2. sin 30°: The value of sin 30° is known to be equal to 1/2. Therefore, sin 30° does not have the same value as cos 30°.
3. cos π/6: The value of cos π/6 is known to be equal to √3/2. Therefore, cos π/6 has the same value as cos 30°.
4. cos 60°: The value of cos 60° is known to be equal to 1/2. Therefore, cos 60° does not have the same value as cos 30°.
In conclusion, the expression that has the same value as cos 30° is cos π/6.