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| Trigonometry |
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Trigonometric
Equations |
The Equations,
sin
(bx + c) = m, -1
<
m <
1,
cos
(bx + c) = m,
-1
<
m <
1,
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tan
(bx
+ c) = m
and
cot
(bx
+ c) = m,
where
b,
c and
m are real
numbers. |
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The
Equation
sin
(bx + c) = m, -1
<
m <
1, example |
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| The Equations,
sin
(bx + c) = m, -1
<
m <
1,
cos
(bx + c) = m, -1
<
m <
1, |
|
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 |
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| Thus, from obtained general solution we can write a common solutions for every given
equation, |
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| The Equation
sin
(bx + c) = m, -1
<
m <
1, example |
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Example: Solve
the equation, |
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Solution: Rewrite
the equation to the form sin
(bx + c) = m, so
sin
(2x + p/6)
= -
1/2
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| An alternative but similar solution can be obtained by substituting the values of,
b,
c
and m,
into |
| x0
= a
and x′0
= p
-
a
and to the common solution
written above |
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| Pre-calculus
contents G |
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