Triangle Properties and Trigonometric Identities

This session introduces the solution of triangles, focusing on the sine and cosine rules. It begins with an overview of the session's objectives, followed by a detailed explanation and derivation of the sine rule. Important trigonometric identities are discussed, which are essential for solving triangle-related problems. The session then covers standard equations and proofs using the sine rule. The cosine rule is introduced, explaining its application in solving triangles with given sides and angles. The session concludes with proving angle relationships using the cosine rule and assigning homework.

What are the six important elements in a triangle?

• Three angles and three vertices

• Three vertices and three sides

• Three medians and three altitudes

• Three sides and three angles

What does the sine rule state in a triangle ABC?

• a/sinA = b/sinB = c/sinC = 2R

• a/sinA = b/sinB = c/sinC = 1/2R

• a/sinA = b/sinB = c/sinC = R

• a/sinA = b/sinB = c/sinC = 1/R

Which identity is used to express sin(A+B)sin(A-B)?

• sin^2A - sin^2B

• tan^2A - tan^2B

• cos^2A - cos^2B

• cot^2A - cot^2B

What is the cosine rule for angle A in a triangle?

• cosA = (a^2 + c^2 - b^2) / (2ac)

• cosA = (b^2 + c^2 + a^2) / (2bc)

• cosA = (a^2 + b^2 - c^2) / (2ab)

• cosA = (b^2 + c^2 - a^2) / (2bc)

If sides of a triangle are 4, 5, and 6, what is the largest angle?

• Three times the smallest angle

• Twice the smallest angle

• Equal to the smallest angle

• Half of the smallest angle