Question

(secθ-cosθ) / sec θ

Answer 1

Do you remember the definition of \(\sec \theta\)?

Answer 2

1/Cos θ

Answer 3

Okay, why don't you rewrite the problem using only cosines?

Answer 4

Please help me math

You are starting a dog-walking business to earn some extra money around your neighborhood. The function r = 10d – d2 gives you the estimated revenue r, that you can expect to earn each day from walking d number of dogs. From past experience, you know that the number of dogs d that you will have the opportunity to walk varies with the price p that you charge per dog given by the equation d = 10 – p.

a. Describe the graph of each function and use the information above to find the greatest amount of revenue that you can expect to receive from walking dogs. It may help you to graph each function separately and label each axis.

Answer 5

It will be a kind of ugly fraction. If you simplify it, it will be nicer :)

Answer 6

ok ((1/cos θ)-(cos θ/1) / (1/cos θ)

Answer 7

\[\frac{\sec \theta - \cos \theta}{\sec \theta} = \frac{\frac{1}{\cos \theta} - \cos \theta}{\frac{1}{\cos \theta} } \]

Answer 8

that is correct. I can get to there but I don't know how to simplify it from there

Answer 9

Dividing by a fraction is the same as multiplying by the reciprocal of the fraction, so that equals
\[(\frac{1}{\cos\theta} - \cos\theta)*\cos\theta\]
Can you take it from there?

Answer 10

Well in in the first part in parentheses, doesn't it cross out to just 1, and that would leave (1) * cosθ ?

Answer 11

I crossmultiplied.. don't know if thats allowed

Answer 12

No, think of this as
\[(\frac{1}{a} - a)*a = \frac{a}{a} - a*a = 1-a^2 \]

Answer 13

You can only cross-multiply if you have an equals sign...
\[\frac{a}{b} = \frac{c}{d}\]What cross-multiplication is is a canned solution to solving that equation:
Multiply both sides by d\[\frac{ad}{b} = c\]Multiply both sides by b\[ad = bc\] and then the last step depends on where the unknown is

Answer 14

so what do you get when you expand that expression instead of cross-multiplying?

Answer 15

It's just distributive property of multiplication:
\[a(b-c) = ab - ac\]although as we have it written, it is\[(b-c)a = ab -ac\]

Answer 16

OK I see it lots better Now.. I think.
Following what you did, I got to 1-cos2θ, right?

Answer 17

if that's \[1-\cos^2\theta\]then yes. does that remind you of any trig identities?

Answer 18

The pyhtagorean identity of Cos2θ + sin2θ is 1.. so
1-cos2θ is sin2θ

Answer 19

really should say sin^2x not sin2x — that's a very different animal!

Answer 20

Oh, sorry. BUt thank you so much.... I will apply this knowledge to the rest of my homework

Answer 21

better yet, use the equation button or learn the little bit of LaTex to typeset the equations. Make it easier for others to help you, and they are more likely to do so :-)

Answer 22

Thanks!

Answer 23

good luck with the homework!