Trigonometry is a branch of mathematics that studies the relationships between the angles and sides of triangles.
It primarily focuses on right-angled triangles, where one angle is exactly 90 degrees.
Sine (sin): In a right triangle, the sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse.
Cosine (cos): The cosine is the ratio of the length of the adjacent side to the hypotenuse.
Tangent (tan): The tangent function is the ratio of the opposite side to the adjacent side.
Cosecant (csc): The reciprocal of sine: csc(θ) = 1/sin(θ)
Secant (sec): The reciprocal of cosine: sec(θ) = 1/cos(θ)
Cotangent (cot): The reciprocal of tangent: cot(θ) = 1/tan(θ)
The key relationship between the sine and cosine of an angle is given by: sin²(θ) + cos²(θ) = 1
For a right triangle with an angle θ:
If the opposite side measures 3 units and the hypotenuse measures 5 units:
sin(θ) = 3/5
cos(θ) = adjacent/hypotenuse (for adjacent side length of 4, cos(θ) = 4/5)
tan(θ) = sin(θ)/cos(θ) = (3/5)/(4/5) = 3/4
Angle of Elevation: The angle formed by the horizontal line and the line of sight to an object above the horizontal.
Angle of Depression: The angle formed by the horizontal line and the line of sight to an object below the horizontal.
Important for solving real-world problems involving heights and distances.
Trigonometry is used in various fields such as physics, engineering, astronomy, and architecture.
It helps in calculating heights of objects, distances between points, and angles of elevation/depression in surveying.
Understanding the fundamental concepts of trigonometry is crucial for solving problems related to triangles and circles.
Mastery of trigonometric identities and functions opens up various avenues for practical applications.