
Trigonometry 

Trigonometric
Equations 
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
Equation
sin
(bx + c) = m, 1
<
m <
1, example 





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
= x_{0}
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, 


The Equation
sin
(bx + c) = m, 1
<
m <
1, example 
Example: Solve
the equation, 


Solution: Rewrite
the equation to the form sin
(bx + c) = m, so
sin
(2x + p/6)
= 
1/2


An alternative but similar solution can be obtained by substituting the values of,
b,
c
and m,
into 
x_{0}
= a
and x′_{0}
= p

a
and to the common solution
written above 









Precalculus
contents G 



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