Simplify Trigonometric Expressions

[nycmathguy]

Section 5.1

Question 19

tan (theta) • cot (theta)/sec (theta)

I will back-substitute for x later.

Let x = theta

tan x = sin x/cos x

cot x = cos x/sin x

The numerator becomes

sin x/cos x • cos x sin x = 1

Our numerator is now 1.

We then have 1/sec x.

I know that 1/sec x = cos x.

Let x = theta

Answer: cos (theta).

You say?

 

[MathLover1]

correct
but, using x gives you more work and it's not helping you

 

[nycmathguy]

correct
but, using x gives you more work and it's not helping you

I know using x is more work but not when compared to typing theta all the time. On paper, I would write the theta symbol, of course.

 

[nycmathguy]

correct
but, using x gives you more work and it's not helping you

How do you like the textbook trip so far?

 

[MathLover1]

I like this part, trigonometry is interesting.

 

[nycmathguy]

I like this part, trigonometry is interesting.

You are right. Trigonometry is beautifully interesting.