Trigonometric Functions and Their Properties Trigonometric functions are a set of six relationships between the sides and angles of triangles. These function...
Trigonometric functions are a set of six relationships between the sides and angles of triangles. These functions allow us to find the values of these side lengths and angles in unknown triangles, which is the primary purpose of trigonometry.
Key trigonometric functions:
Sine (sin θ): The ratio of the side opposite to θ to the total side length.
Cosine (cos θ): The ratio of the side adjacent to θ to the total side length.
Tangent (tan θ): The ratio of the side opposite to θ to the side adjacent to θ.
Cotangent (cot θ): The ratio of the side adjacent to θ to the side opposite to θ.
Sine cosine (sin cos θ): The product of the sine and cosine of an angle.
Cosine sine (cos sin θ): The product of the cosine and sine of an angle.
These functions can be used to find missing side lengths and angles in right triangles, as well as solve problems involving triangles with known angles.
Properties of trigonometric functions:
The sine, cosine, and tangent functions are all positive in the first quadrant, while the cotangent, sine cosine, and cosine sine are all positive in the second quadrant.
The sum of the angles in a triangle is always 180 degrees.
The sine, cosine, and tangent functions are reciprocals of each other.
The sine and cosine functions are the projections of the opposite and adjacent sides of a triangle onto the opposite side, respectively.
The tangent function is the projection of the opposite side onto the adjacent side.
These properties help to simplify trigonometric expressions and solve trigonometric problems in various ways