Can somebody explain how trigonometric form polar equations are divided/multiplied?

Attachment 1 : Option C

Attachment 2 : Option A

Step-by-step explanation:

( 1 ) Expressing the product of z1 and z2 would be as follows,

Now to solve such problems, you will need to know what cos(π / 5) is, sin(π / 5) etc. If you don't know their exact value, I would recommend you use a calculator,

cos(π / 5) = ,

sin(π / 5) =

cos(3π / 2) = 0,

sin(3π / 2) = - 1

Let's substitute those values in our expression,

And now simplify the expression,

The exact value of = and = Therefore we have the expression , which is close to option c. As you can see they approximated the solution.

( 2 ) Here we will apply the following trivial identities,

cos(π / 3) = ,

sin(π / 3) = ,

cos(- π / 6) = ,

sin(- π / 6) =

Substitute into the following expression, representing the quotient of the given values of z1 and z2,

⇒

The simplified expression will be the following,

or in other words or

The solution will be option a, as you can see.

c. side angle side. u shares the same sides