Sine Theta (sin θ) = opposite/hypotenuse = a/c
Cosine Theta (cos θ) = adjacent/hypotenuse = b/c
Tangent Theta (tan θ) = opposite/adjacent = a/b
Cotangent Theta (cot θ) = adjacent/opposite = b/a
Secant Theta (sec θ) = hypotenuse/adjacent = c/b
Cosecant Theta (csc θ) = hypotenuse/opposite = c/a
You may need to look on the link below for some sample calculations
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There are three types of trigonometric functions, they are: 1- Plane Trigonometric Functions 2- Inverse Trigonometric Functions and 3- Hyperbolic Trigonometric Functions
trigonometric table gives the values of all the trigonometric functions for any angle. i.e; it gives the numerical values of sine, cosine, tangent etc for any angle between 0 to 180 degrees the values for other angles can be calculated using these.
In geometry, similar shapes have the same angles. This means that the values of the basic trigonometric functions of these angles are the same.
With ease, I suppose. The question depends on what you consider easy trigonometric functions.
Vectors.