Simplifying Trig Expressions Worksheet
Simplifying Trig Expressions Worksheet
We use the Trigonometric formulas and identities to simplifying trig expressions that are part
of the mathematics .
When we talk about the trigonometry it defines the relation between the sides and angles of
the triangle and it will help in solving such complex expression that is normal y not solve by
any other method rather than trigonometric formulas .
So for simplifying trig expressions we have to know about al the formulas of trigonometry
.Some of the trigonometric formulas are as fol ows:
sin = perpendicular / hypotenuse
cos = Base / hypotenuse
tan = perpendicular / Base .
The above functions are define for the acute angles and there are some other types of
functions also as functions for the Arbitrary angles or for special triangles.
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These categorization is based on the different types of shapes of the triangles and for different
types of angles that are drawn in these triangles .
There are also some laws of Trigonometric functions as sine and cos etc .that are define as
fol ows:
If there is a triangle ABC then according to the sine law
Sin A / a = Sin B / b = sin C / c here in the given law (A, B and C are the angles in the triangle
ABC and a, b and c are define the side of the triangle ABC.)
There is also defining some of the law based on the cos function that is as follows:
a^2 = b^2 + c^2 - 2 b c cos A
b^2 = a^2 + c^2 - 2 a c cos B
c^2 = a^2 + b^2 - 2 a b cos C
(A, B and C are the angles in the triangle ABC and a, b and c are define the side of the
triangle ABC.)
We can also define the relation between the different trigonometric function as:
csc a = 1/ sin a
sin a = 1 / csc a
tan a = 1 / cot a
cot a = 1 / tan a
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sec a = 1 / cos a
cos a = 1 / sec a
So there are different types of formulas in trigonometry that are helps in simplifying trig
expressions that are explained as fol ows:
If there is an expression to solve: sin (-a) cos (Pi / 2 -a)?
Solution: As according to the identity sin (-a) = - sin (a) and cos ( Pi / 2 - a) = sin (a) then
simplify the given expression as
sin ( -a) cos ( Pi / 2 -a ) = - sin (a) sin (a) = - sin 2 a.
There is one other expression to solve as sin 2 a - cos 2 a sin 2 a .
Solution: As we can factor the above expression by sin2 a and simplify it
sin 2 a - cos 2 a sin 2 a
= sin2 a ( 1 - cos2 a) as we know ( 1 - cos2 a) = sin 2 a )
= sin 4 a .


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