University:
Stanford University
Course:
Introduction to Mathematical Thinking
Academic year:

2023
Views:

305

Pages:

2
Author:

agata robin

Study Note for Trigonometry Trigonometry is a branch of mathematics that studies the relationship between the sides and angles of triangles. Trigonometry is widely used in geometry, astronomy, surveying, navigation and many other fields. Basic Concepts of Trigonometry: Trigonometry Ratios: Comparisons between the sides of triangles. There are 3 main trigonometric ratios: Sine (sin) = front side/hypotenuse Cosine (cos) = side side/hypotenuse Tangent (tan) = front side/side side Special angles of a triangle: The angles 0, 30, 45, 60, 90 degrees have unique and important trigonometric ratio values. Trigonometric Identities: Important formulas like sin^2(x) + cos^2(x) = 1 Trigonometric Functions: Sine, cosine, tangent, cosecant, secant, and cotangent functions that relate angles to trigonometric ratios. Trigonometric Equations: Equations that contain one or more trigonometric functions. By understanding these basic trigonometry concepts, we can solve various problems of triangles and circles related to angles and distances. Trigonometry has many benefits and applications in both mathematics and everyday life. Table Spacial Angle Angle (degrees) 0 30 45 60 90 Sine 0 0.5 0.707 0.866 1 Cosine 1 0.866 0.707 0.5 0 Tangent 0 0.577 1 1.732 - Question: It is known that triangle ABC has sides AB = 8 cm, BC = 6 cm, and angle A = 30°. Define: a. Cos A value b. Sin C value c. AC side length Discussion: a. Cos A = side / hypotenuse = AB / AC We don't know the length of AC, but we do know the angle A = 30° Cos 30° = 0.866 (from the trigonometry table) So, Cos A = 0.866 b. Sin C = opposite side / hypotenuse = BC / AC AC is unknown, but based on trigonometric identities: sin^2 C + cos^2 C = 1 cos^2 C = 0.866^2 = 0.75 1 - 0.75 = 0.25 sin C = √0.25 = 0.5 c. Use Pythagoras on triangle ABC: AB^2 + BC^2 = AC^2 8^2 + 6^2 = AC^2 64 + 36 = 100 AC = 10 cm So, the conclusion: Cos A = 0.866 SinC = 0.5 AC = 10 cm