ENEM Practice: Trigonometry Basics

ENEM Practice Objective

This exercise aims to enhance your ability to solve basic trigonometric equations, an essential skill for the Mathematics section of the ENEM exam. As you work through these exercises, consider how trigonometry is utilized in traditional Chinese astronomy for calculating distances and angles between celestial bodies.

Exercise Content

Trigonometry has had applications in various fields, including astronomy, which has been important in traditional Chinese culture. The calculations used for charting stars and planets often employ trigonometric equations.

Multiple-Choice Questions

1. Solve the equation \( \sin(x) = 0.5 \).

   1. \( x = 30^\circ \)
   2. \( x = 45^\circ \)
   3. \( x = 60^\circ \)
   4. \( x = 90^\circ \)

2. Find the value of \( \cos(60^\circ) \).

   1. \( \frac{1}{2} \)
   2. \( \frac{\sqrt{3}}{2} \)
   3. \( 0 \)
   4. \( 1 \)

Discursive Questions

1. Describe a real-world application of trigonometry in astronomy. Take 5 minutes to write your explanation.

Answer Key

Multiple-Choice Questions

1. Answer: A. \( x = 30^\circ \)
2. Answer: A. \( \frac{1}{2} \)

Discursive Questions

1. One real-world application of trigonometry in astronomy involves calculating the distance of a star from Earth. By observing the star from two different points and measuring the angle of elevation, astronomers can use trigonometric functions to estimate the star’s distance.