Definition of Trigonometric Equations
Suppose
that given the equation sin2 x + cos2 x = 1 and ask for the value of x that satisfies the
equation. It turns out that for each x value it always fulfills. Such an equation
is called identity. In trigonometry other than identity there is also a form of
equation that only applies to the values of certain variables.
In your
school you must have learned about the functions of sine, cosine, and tangent
which are periodic functions. An example is a sine function said to have a 360
period, if and only if α0 = sin
(α + n . 360)0, n integers. This means that the value of the
trigonometric function always repeats every plus or minus multiples of 360. You
also know the periods of cosine functions and tangents respectively are 360
and 180. Based on this information, the following rules can be used to solve
the trigonometric equation.
1. If sin x0 = sin α0, then x = α + n . 360 or,
x = (180 – α) + n . 360
2. if cos x0 = cos α0, then x = α + n . 360 or,
x = - α + n . 360
3. if tan x0 = tan α0, then x = α + n . 180 with n ∈ interger.
4. if a sin x0 = 0 then x = k . 180
5. if b cos x0 = 0 then x = 900 = ± k . 180
6. if c tan x0 = 0 then x = k . 180 with k ∈ interger.
1. If sin x0 = sin α0, then x = α + n . 360 or,
x = (180 – α) + n . 360
2. if cos x0 = cos α0, then x = α + n . 360 or,
x = - α + n . 360
3. if tan x0 = tan α0, then x = α + n . 180 with n ∈ interger.
4. if a sin x0 = 0 then x = k . 180
5. if b cos x0 = 0 then x = 900 = ± k . 180
6. if c tan x0 = 0 then x = k . 180 with k ∈ interger.
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