PRAXIS Core Math Exam Prep

Explanation
Trigonometry is the branch of mathematics that focuses on figures with three sides and angles. It deals with the relationships between the sides and angles of triangles, and it is used to solve problems involving angles and distances. Trigonometry is essential in fields such as physics, engineering, and navigation, where understanding the properties of triangles is crucial.

Explanation
Calculus is the branch of mathematics that measures the degree of changes. It deals with the concepts of differentiation and integration, which help in understanding and quantifying how quantities change over time or space. By using calculus, one can determine rates of change, slopes, and areas under curves, making it an essential tool in analyzing and predicting various phenomena in fields such as physics, engineering, economics, and biology.

Explanation
Set theory was founded in 1874. This is the year when the German mathematician Georg Cantor published his groundbreaking work on set theory, which laid the foundation for this branch of mathematics. Cantor's work introduced the concept of sets and their properties, and he developed the notion of cardinality and infinite sets. His work revolutionized mathematics and had a profound impact on various fields such as logic, analysis, and algebra.

Explanation
Descriptive set theory is the study of subsets of the real line and their properties. It focuses on classifying and analyzing these subsets based on their complexity and definability. This field of study is concerned with understanding the structure and behavior of sets in the context of real analysis and measure theory. It has applications in various areas of mathematics, including logic, set theory, and topology.

Explanation
The word "mathematics" originated from the Greek language. The Greek word "mathematikos" means "inclined to learn" or "studious." The Greeks made significant contributions to the field of mathematics, with famous mathematicians like Euclid, Pythagoras, and Archimedes. The word "mathematics" reflects the Greek influence and their emphasis on the study and understanding of numbers, shapes, and patterns.

Explanation
A cardinal number with an extra property is called a "large cardinal." Large cardinals are special types of infinite cardinal numbers that possess additional properties beyond the standard properties of cardinal numbers. These additional properties make them important in set theory and mathematical logic.

Explanation
Paul Cohen is the correct answer because he was a prominent mathematician who made significant contributions to set theory, specifically in the area of forcing. He developed the method of forcing in the 1960s, which revolutionized the study of set theory by providing a powerful tool for constructing models of different set-theoretic assumptions. His work on forcing had a profound impact on the field and earned him the Fields Medal in 1966.

Explanation
The value of the angle on a straight line is always 180°. This is because a straight line forms a straight angle, and by definition, a straight angle measures 180°. Therefore, the correct answer is 180°.

Explanation
Trigonometry is a branch of mathematics that deals with the relationships between the angles and sides of triangles. Pharmacy, medical imaging, and architecture all involve the use of trigonometry principles. However, quantity surveying does not typically require the use of trigonometry. Quantity surveying is a profession that involves estimating and managing costs and quantities in construction projects, and it primarily relies on knowledge of construction materials, labor costs, and project management rather than trigonometry principles.

Explanation
The Pythagorean identities are mathematical equations that relate the trigonometric functions of a right triangle. There are three main Pythagorean identities: sine squared plus cosine squared equals one, tangent squared plus one equals secant squared, and cotangent squared plus one equals cosecant squared. These identities are fundamental in trigonometry and are used to simplify and solve trigonometric equations.