Trigonometry is a branch of mathematics that deals with the relationships between the angles and sides of triangles. It has wide applications in various fields, including physics, engineering, and computer science. Here are some basic concepts in trigonometry:
Unit Circle
- The unit circle is a circle with a radius of 1 unit, centered at the origin of a coordinate system.
- Trigonometric functions can be defined using the unit circle. For a point (x, y) on the unit circle, the coordinates (cos θ, sin θ) represent the values of the cosine and sine functions, respectively, at an angle θ with the positive x-axis.
- Sine (sin θ): In a right-angled triangle, the sine of an angle is the ratio of the length of the side opposite the angle to the hypotenuse.
- Cosine (cos θ): The cosine of an angle is the ratio of the length of the adjacent side to the hypotenuse in a right-angled triangle.
TRIGONOMETRIC FUNCTIONS
- Tangent (tan θ): Tangent is the ratio of the length of the side opposite the angle to the adjacent side in a right-angled triangle.
- Cosecant (csc θ), Secant (sec θ), Cotangent (cot θ): These are the reciprocals of sine, cosine, and tangent, respectively.
Trigonometric Identities:
Pythagorean Identities Reciprocal Identities
- sin^2θ + cos^2θ = 1 - cscθ = 1/sinθ
- 1 + tan^2θ = sec^2θ - secθ = 1/cosθ
- 1 + cot^2θ = csc^2θ - cotθ = 1/tanθ
Quotient and Co-Function Identities
- tanθ = sinθ/cosθ - secθ = 1/cosθ
- cotθ = cosθ/sinθ - cscθ = 1/sinθ
Understanding these fundamental concepts enables the calculation of trigonometric values and the simplification of expressions involving trigonometric functions in various mathematical and scientific contexts.