Trigonometric Functions of Angles

1. The Law of Cosine

1.1. In any triangle ABC , we have

1.2. a^2 + b^2 + c^2 = 2bc cos A

1.3. b^2 + a^2 + c^2 = 2ac cos B

1.4. c^2 + a^2 + b^2 = 2ab cos C

2. Heron's Formula

2.1. The area of a triangle ABC is given by

2.2. Area = √s(s - a)(s - b)(s - c)

2.3. where s = 1 / 2(a + b + c) is the semiperimeter of the triangle [s is half the perimeter]

3. Area of a triangle

3.1. The area of a triangle with sides of lengths a and b and with included angle u is

3.2. Area = 1 / 2 ab sin θ

4. cos θ = adjacent / hypotenuse

4.1. sec θ = hypotenuse / adjacent

5. 1. To convert degrees to radians, multiply by π / 180

6. Area of a circular sector

6.1. In a circle of radius r, the area A of a sector with a central angle of u radians is

6.2. A = 1 / 2 r^2 θ

7. Angle measure

7.1. Relationship between Degrees and Radians

7.2. 180 degree = π rad 1 π = (180 / π) degree 1 degree = π / 180 rad

7.3. 2. To convert radians to degrees, multiply by 180 / π

8. Trigonometry of Right Triangles

8.1. sin θ = opposite / hypotenuse

8.1.1. csc θ = hypotenuse / opposite

8.2. tan θ = opposite / adjacent

8.2.1. cot θ = adjacent / opposite