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| Trigonometry |
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Trigonometric
Equations |
The Equations,
tan
(bx
+ c) = m
and
cot
(bx
+ c) = m,
where
b,
c and
m are real
numbers.
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The
Equation
tan
(bx
+ c) = m, example |
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| The Equations,
tan
(bx
+ c) = m
and
cot
(bx
+ c) = m,
where
b,
c
and m
are real numbers. |
| The given equations can be written as F(bx +
c) = m
where F
substitutes a trigonometric function, x
is an arc
to be calculated and m
is a value of a given trigonometric function. |
| To every trigonometric function we can determine an arc, a +
k · P of which function value equals
m
that is F(a +
k · P) = m,
where a
= x0
is the basic solution, and P
is the period, then |
| F(bx +
c) = F(a +
k · P)
or bx +
c = a +
k · P,
thus |
 |
| Thus, from obtained general solution we can write a common solutions for every given
equation, |
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| The Equation
tan
(bx
+ c) = m, example |
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Example: Solve
the equation, |
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Solution: Rewrite
the equation to the form tan
(bx + c) = m,
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| We obtain the same result if we put given parameters,
b,
c, and corresponding basic solution |
| x0
= a
= tan-1
m to the common
solution that is, b
= 1/3,
c = -
p/2 and
x0
= a
= tan-1(-Ö3/3) =
-
p/6 |
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| Pre-calculus contents
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