This is a free lesson from our course in Trigonometry
In this lesson you'll explore how to solve trigonometric equations consisting of trigonometric functions. This will be done with the
help of some examples, practice questions with solution and using video explanation
by the instructor in own handwriting. Step by step solving trigonometric equations
requires simplification techniques and use of earlier learnt algebra because both
principles are related.
A trigonometric equation is one that involves one or more of the six functions sine, cosine, tangent, cotangent, secant, and cosecant.Solving trigonometric equations could be of two types: A
simple trigonometric equation or trigonometric identities. Identities are true for any angle, whereas conditional equations may be true only
for certain angles.(More text below video...)
(Continued from above)
Trigonometric equation can be solved analytically, here are
the steps you can follow to do that:
• put the equation in terms of one function of one angle.
• write the equation as one trig function of an angle equals a constant.
• write down the possible value(s) for the angle.
• if necessary, solve for the variable.
• apply any restrictions on the solution.
For example, to solve 2 cos x + 1 = 0, for all values of x such
that 0 < x <
, you isolate x
in the same way you normally would do and then can write x = cos-1(-1/2).
Since, the cosine function in quadrant II gives negative value, so x =
120
which is same as 2/3
radians.
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, you isolate x
in the same way you normally would do and then can write x = cos-1(-1/2).
Since, the cosine function in quadrant II gives negative value, so x =
120
which is same as 2