Trigonometry
Trigonometric Equations
sin (bx + c) = m,  -1 <  m < 1,      cos (bx + c) = m,  -1 <  m < 1,
tan (bx + c) = m    and    cot (bx + c) = mwhere b, c and m are real numbers.
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 = 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,
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
x0 = a  and  x0 = p - a  and to the common solution written above
Pre-calculus contents G