Trigonometry Basics

Study Notes

Trigonometry is the branch of mathematics that deals with the relationships between the sides and angles of triangles.
It involves the use of trigonometric functions such as sine, cosine, and tangent to describe these relationships.

Sine (sin): The ratio of the opposite side to the hypotenuse of a right-angled triangle.
- sin(A) = opposite side / hypotenuse
Cosine (cos): The ratio of the adjacent side to the hypotenuse of a right-angled triangle.
- cos(A) = adjacent side / hypotenuse
Tangent (tan): The ratio of the opposite side to the adjacent side of a right-angled triangle.
- tan(A) = opposite side / adjacent side
Cosecant (csc): The reciprocal of sine.
- csc(A) = 1 / sin(A)
Secant (sec): The reciprocal of cosine.
- sec(A) = 1 / cos(A)
Cotangent (cot): The reciprocal of tangent.
- cot(A) = 1 / tan(A)

Pythagorean Identity: sin^2(A) + cos^2(A) = 1
Sum and Difference Formulas:
- sin(A + B) = sin(A)cos(B) + cos(A)sin(B)
- sin(A - B) = sin(A)cos(B) - cos(A)sin(B)
- cos(A + B) = cos(A)cos(B) - sin(A)sin(B)
- cos(A - B) = cos(A)cos(B) + sin(A)sin(B)

Sine and Cosine Graphs:
- Period: 2π
- Amplitude: 1
Tangent Graph:
- Period: π
- Asymptotes: x = π/2 + kπ, where k is an integer

Right Triangles:
- Use trigonometric functions to find missing sides and angles.
Oblique Triangles:
- Use the Law of Sines or the Law of Cosines to find missing sides and angles.
- Law of Sines: a / sin(A) = b / sin(B) = c / sin(C)
- Law of Cosines: c^2 = a^2 + b^2 - 2ab * cos(C)

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles, involving trigonometric functions such as sine, cosine, and tangent.

Sine (sin) is the ratio of the opposite side to the hypotenuse of a right-angled triangle, calculated as sin(A) = opposite side / hypotenuse.
Cosine (cos) is the ratio of the adjacent side to the hypotenuse of a right-angled triangle, calculated as cos(A) = adjacent side / hypotenuse.
Tangent (tan) is the ratio of the opposite side to the adjacent side of a right-angled triangle, calculated as tan(A) = opposite side / adjacent side.
Cosecant (csc) is the reciprocal of sine, calculated as csc(A) = 1 / sin(A).
Secant (sec) is the reciprocal of cosine, calculated as sec(A) = 1 / cos(A).
Cotangent (cot) is the reciprocal of tangent, calculated as cot(A) = 1 / tan(A).

Pythagorean Identity: sin^2(A) + cos^2(A) = 1.
Sum and Difference Formulas:
- sin(A + B) = sin(A)cos(B) + cos(A)sin(B)
- sin(A - B) = sin(A)cos(B) - cos(A)sin(B)
- cos(A + B) = cos(A)cos(B) - sin(A)sin(B)
- cos(A - B) = cos(A)cos(B) + sin(A)sin(B)

Sine and Cosine Graphs:
- Have a period of 2π
- Have an amplitude of 1
Tangent Graph:
- Has a period of π
- Has asymptotes at x = π/2 + kπ, where k is an integer

Right Triangles:
- Use trigonometric functions to find missing sides and angles
Oblique Triangles:
- Use the Law of Sines or the Law of Cosines to find missing sides and angles
- Law of Sines: a / sin(A) = b / sin(B) = c / sin(C)
- Law of Cosines: c^2 = a^2 + b^2 - 2ab * cos(C)