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    Mathematics - Trigonometry - Trigonometric Functions

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    How do you figure out trigonometric functions?

    © BrainMass Inc. brainmass.com December 24, 2021, 7:49 pm ad1c9bdddf
    https://brainmass.com/math/trigonometry/mathematics-trigonometry-trigonometric-functions-222158

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    How do you figure out trigonometric functions?

    Sin, Cos and Tan functions

    The trigonometric functions of angles are the ratios of the various sides of a triangle. Consider a right-angled triangle ABC as shown in the figure below.

    The following terminology is useful.
    • Hypotenuse: The side opposite to the right angle in a triangle is called the hypotenuse. Here the side AC is the hypotenuse.
    • Opposite Side: The side opposite to the angle in consideration is called the opposite side. So, if we are considering angle A, then the opposite side is CB.
    • Base: The third side of the triangle, which is one of the arms of the angle under consideration, is called the base. If A is the angle under consideration, then the side AB is the base.

    For angle A (sometimes referred to as angle CAB), the following fundamental trigonometric functions can be defined.
    Sine of A = sin A = Opposite Side / Hypotenuse = CB/CA = a/b
    Cosine of A = cos A = Base / Hypotenuse = AB/CA = c/b
    Tangent of A = tan A = Opposite Side / Base = CB/AB = a/c

    From the definitions, it can be seen that tan A = sin A / cos A.

    Cosec, Sec and Cot Functions

    A few more useful functions can be defined.
    Cosecant of A = cosec A = 1 / sin A = b/a
    Secant of A = sec A = 1 / cos A = b/c
    Cotangent of A = cot A = 1 / tan A = c/a

    From the definitions, it can be seen that cot A = cosec A / sec A

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com December 24, 2021, 7:49 pm ad1c9bdddf>
    https://brainmass.com/math/trigonometry/mathematics-trigonometry-trigonometric-functions-222158

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