Accuplacer Practice Test

If θ is an acute angle and sin θ = 1/2, then cos θ =

1. -1

2. 0

3. 1/2

4. √3/2

The correct answer is: √3/2

When considering the relationship between the sine and cosine functions in a right triangle, both functions can be derived from the same angle. Since \( \sin \theta = \frac{1}{2} \) and \( \theta \) is an acute angle, we can recall the sine values of special angles. The sine of \( 30^\circ \) (or \( \frac{\pi}{6} \) radians) is \( \frac{1}{2} \). In a right triangle corresponding to this angle, the cosine can also be found. The cosine function measures the ratio of the length of the adjacent side to the hypotenuse. For an angle of \( 30^\circ \), using the properties of a 30-60-90 triangle, the length of the adjacent side (the side opposite the \( 60^\circ \) angle) is \( \sqrt{3} \) when the hypotenuse is \( 2 \). Therefore, \[ \cos 30^\circ = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{\sqrt{3}}{2}. \] Thus, with \( \sin \theta = \frac{1