Simplifying Trig Expressions Worksheet

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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.

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

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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