Free Pre-Calculus Trigonometry Questions and Answers

Question 1

Find the length of AC for the given triangle if tan(x) = 40/9.

Accepted Answer

41

Answer

Given tan(x) = 40/9, this means the opposite side (BC) is 40 and the adjacent side (AB) is 9 in a right triangle. To find the hypotenuse (AC), use the Pythagorean theorem: AC^2 = AB^2 + BC^2. So, AC^2 = 9^2 + 40^2 = 81 + 1600 = 1681. Taking the square root of 1681 gives AC = 41.

Question 2

Which way do you measure a positive angle?

Accepted Answer

Counterclockwise

Answer

In trigonometry and mathematics, positive angles are conventionally measured by rotating the terminal side counterclockwise from the positive x-axis. This standard convention helps maintain consistency in angle definitions and trigonometric functions across different quadrants. Clockwise rotation, conversely, defines negative angles.

Question 3

Determine the degree size of one complete revolution.

Accepted Answer

360

Answer

One complete revolution around a circle is defined as 360 degrees. This measurement system divides a circle into 360 equal parts, with each part representing one degree. This convention is widely used in geometry, navigation, and many engineering applications.

Question 4

Which measurement system is most commonly used to express the size of an angle?

Accepted Answer

Degrees

Answer

The degree system is the most commonly used unit for expressing the size of an angle in everyday contexts and many practical applications. While radians are fundamental in higher mathematics and calculus, degrees provide a more intuitive and easily visualized measure for general use. A full circle is 360 degrees, a half circle is 180 degrees, and a quarter circle is 90 degrees.

Question 5

What is the approximate value of π (pi) ?

Accepted Answer

3.14

Answer

Pi (π) is a mathematical constant representing the ratio of a circle's circumference to its diameter. Its approximate value is 3.14159, but for most calculations, 3.14 is a sufficiently accurate approximation. This value is fundamental in geometry and trigonometry, appearing in formulas for areas, volumes, and arc lengths.

PRE CALCULUS Practice Test

PRE CALCULUS Practice Test

Free Pre-Calculus Trigonometry Questions and Answers