Simplifying Trig Expressions Exit Slips

Simplify the expression

Answer explanation

Here are the first two steps you could have taken to solve for the answer.

Notice that something can cancel out and you can then use a Pythagorean identity.

Simplify the expression. (Hint: You should get just a number as your answer)

(a)  

Answer explanation

This is the first step you could take.

After this notice that if you multiply the like terms it should look like one of the Pythagorean identities.

Simplify the expression

Answer explanation

Here are the first 2 steps you can take to simplify.

After this notice how something can cancel out and there is nothing else that can be done.

Simplify the expression

Answer explanation

Here are the first 3 steps you can take to simplify.

At this point, there is something that can be simplified further and then don't forget your reciprocal identities.

Simplify the following expression

Answer explanation

This one is a little trickier so I am showing all the steps I would have taken to solve this one.

This could have been approached in a slightly different manner so if there are any questions please ask.

Simplify

• sin²θ

• cosθ

• tanθ

• 1- sin²θ

Answer explanation

This one should be pretty simple, rewrite cot and you should see what cancels out and what is left over.

Simplify

• -1

• sin θ

• csc θ

• 1

• 2

Answer explanation

Rewrite cot and sec.

Should hopefully be pretty obvious after that.

Simplify

• csc²θ

• sec²θ

• cscθ

• 1

Answer explanation

There is a Pythagorean identity and I would also advise rewriting cot2x.

After that you should see several things cancel out.