Trigonometry Basics

Trigonometry

Sine, Cosine, and Tangent

• Sine (sin): Ratio of the opposite side to the hypotenuse in a right-angled triangle.
  • sin(A) = opposite side / hypotenuse
• Cosine (cos): Ratio of the adjacent side to the hypotenuse in a right-angled triangle.
  • cos(A) = adjacent side / hypotenuse
• Tangent (tan): Ratio of the opposite side to the adjacent side in a right-angled triangle.
  • tan(A) = opposite side / adjacent side

Angles and Triangles

• Right-angled triangle: A triangle with one right angle (90°).
• Angle of elevation: The angle between the line of sight and the horizontal when looking up at an object.
• Angle of depression: The angle between the line of sight and the horizontal when looking down at an object.
• Reference angle: The acute angle between the terminal side of an angle and the x-axis.

Solving Triangles

• Pythagorean identity: sin^2(A) + cos^2(A) = 1
• Sine rule: a / sin(A) = b / sin(B) = c / sin(C) (for any triangle with sides a, b, c and angles A, B, C)
• Cosine rule: a^2 = b^2 + c^2 - 2bc * cos(A) (for any triangle with sides a, b, c and angle A)
• Trigonometric identities: equations that are true for all values of the variables, such as sin(A) = cos(90° - A)

Trigonometry

Sine, Cosine, and Tangent

• Sine (sin): The ratio of the opposite side to the hypotenuse in a right-angled triangle, calculated as sin(A) = opposite side / hypotenuse.
• Cosine (cos): The ratio of the adjacent side to the hypotenuse in a right-angled triangle, calculated as cos(A) = adjacent side / hypotenuse.
• Tangent (tan): The ratio of the opposite side to the adjacent side in a right-angled triangle, calculated as tan(A) = opposite side / adjacent side.

Angles and Triangles

• Right-angled triangle: A triangle with one right angle (90°), used as a basis for trigonometric calculations.
• Angle of elevation: The angle between the line of sight and the horizontal when looking up at an object, used to calculate trigonometric values.
• Angle of depression: The angle between the line of sight and the horizontal when looking down at an object, used to calculate trigonometric values.
• Reference angle: The acute angle between the terminal side of an angle and the x-axis, used to simplify trigonometric calculations.

Solving Triangles

• Pythagorean identity: A fundamental equation in trigonometry, sin^2(A) + cos^2(A) = 1, which relates the sine and cosine of an angle.
• Sine rule: A formula used to solve triangles, a / sin(A) = b / sin(B) = c / sin(C), where a, b, and c are side lengths and A, B, and C are angles.
• Cosine rule: A formula used to solve triangles, a^2 = b^2 + c^2 - 2bc * cos(A), where a, b, and c are side lengths and A is an angle.
• Trigonometric identities: Equations that are true for all values of the variables, such as sin(A) = cos(90° - A), used to simplify trigonometric calculations and solve problems.