Understanding Theorems and Proofs

Which of the following best describes a theorem in mathematics?

• A statement that is assumed to be true without proof.

• A statement in mathematics that has been proven to be true.

• A hypothesis that is yet to be tested.

• A mathematical equation involving variables.

In trigonometry, which function is used to find the ratio of the opposite side to the hypotenuse in a right triangle?

• Cosine

• Tangent

• Sine

• Secant

Which of the following is an example of circular reasoning?

• Using a logical argument to prove a theorem.

• Stating that "The sky is blue because it is blue."

• Solving a trigonometric equation using identities.

• Proving a statement by contradiction.

What is the primary focus of trigonometry in mathematics?

• The study of algebraic expressions.

• The relationships between the sides and angles of triangles.

• The calculation of derivatives and integrals.

• The exploration of geometric shapes.

Which of the following statements is true about a mathematical proof?

• It is a guess based on observation.

• It is a logical argument that shows a statement is true.

• It is a formula used to calculate angles.

• It is a type of flawed logic.