Trigonometry - Basic Notes
1. What is Trigonometry?
Trigonometry is the branch of mathematics that deals with the relationships between the angles and sides of
triangles, especially right-angled triangles.
2. Basic Trigonometric Ratios:
- Sine (sin): Opposite / Hypotenuse
- Cosine (cos): Adjacent / Hypotenuse
- Tangent (tan): Opposite / Adjacent
- Cosecant (csc): 1 / sin
- Secant (sec): 1 / cos
- Cotangent (cot): 1 / tan
3. Trigonometric Identities:
- sin^2(theta) + cos^2(theta) = 1
- 1 + tan^2(theta) = sec^2(theta)
- 1 + cot^2(theta) = csc^2(theta)
4. Angle Measures:
Angles can be measured in degrees or radians.
- 180 degrees = pi radians
- 1 degree = pi / 180 radians
5. Values of Trigonometric Ratios:
Standard angles: 0, 30, 45, 60, and 90
- sin(0) = 0, sin(30) = 1/2, sin(45) = 1/sqrt(2), sin(60) = sqrt(3)/2, sin(90) = 1
- Similarly, memorize values for other functions.
6. Applications of Trigonometry:
- Solving triangles
- Height and distance problems
- Physics (waves, oscillations, etc.)
- Engineering and astronomy
1. What is Trigonometry?
Trigonometry is the branch of mathematics that deals with the relationships between the angles and sides of
triangles, especially right-angled triangles.
2. Basic Trigonometric Ratios:
- Sine (sin): Opposite / Hypotenuse
- Cosine (cos): Adjacent / Hypotenuse
- Tangent (tan): Opposite / Adjacent
- Cosecant (csc): 1 / sin
- Secant (sec): 1 / cos
- Cotangent (cot): 1 / tan
3. Trigonometric Identities:
- sin^2(theta) + cos^2(theta) = 1
- 1 + tan^2(theta) = sec^2(theta)
- 1 + cot^2(theta) = csc^2(theta)
4. Angle Measures:
Angles can be measured in degrees or radians.
- 180 degrees = pi radians
- 1 degree = pi / 180 radians
5. Values of Trigonometric Ratios:
Standard angles: 0, 30, 45, 60, and 90
- sin(0) = 0, sin(30) = 1/2, sin(45) = 1/sqrt(2), sin(60) = sqrt(3)/2, sin(90) = 1
- Similarly, memorize values for other functions.
6. Applications of Trigonometry:
- Solving triangles
- Height and distance problems
- Physics (waves, oscillations, etc.)
- Engineering and astronomy
