Question

The expression csctheta-sinthetais equivalent to what?

Answer 1

\[\large \csc \theta-\sin \theta\]

Remember your identity for cosecant? You can rewrite it terms of sine.

Answer 2

i know csctheta is 1/sin theta but i dont know what to do

Answer 3

\[\large \frac{1}{\sin \theta}-\sin \theta\]Ok from here, combine the fractions. Get a common denominator.

Answer 4

\[\large \frac{1}{\sin \theta}-\frac{\sin\theta}{1}\]

Understand how to do that?

Answer 5

why did we flip the right side?/

Answer 6

I didn't flip it.
I'm just try to show you that \(\large 5\) is the same thing as \(\large \dfrac{5}{1}\).

Maybe that way it will be easier for you to realize that they're both fractions. And can be combined.

Answer 7

ok..and find the common denominator which is 1 and sin theta

Answer 8

yah that sounds right, so we need to multiply the right fraction by \(\large \dfrac{\sin\theta}{\sin\theta}\),
while the left fraction needs to be multiplied by 1/1 (so we can leave it alone).

Answer 9

\[\large \frac{1}{\sin \theta}-\frac{\sin\theta}{1}\color{royalblue}{\left(\frac{\sin\theta}{\sin\theta}\right)} \qquad = \qquad \frac{1}{\sin\theta}-\frac{\sin^2\theta}{\sin\theta} \qquad = \qquad \frac{1-\sin^2\theta}{\sin\theta}\]

Confused about any of that?
The blue term is the one we used to get a common denominator.

Answer 10

would the answer be 1?

Answer 11

No :o

Answer 12

it has a)1/sin theta x
b)1
c)sintheta/cos^2theta
d)cottheta costheta

Answer 13

we haven't finished the problem yet..

Answer 14

was trying to see if you're following any of this before going further :o

Answer 15

ohh so sin theta divided by sintheta is the lcd and you multiply it bythe sintheta/1

Answer 16

ya :o

Answer 17

ok i c

Answer 18

\[\large \frac{1-\sin^2\theta}{\sin\theta}\]

From here it's all about remembering identities.
There are 2 identities that we'll apply to match one of the answers.

Do you remember an identity for this?
\(\large 1-\sin^2\theta=?\)

Answer 19

cos^2 theta

Answer 20

\[\large \frac{1-\sin^2\theta}{\sin\theta} \qquad = \qquad \frac{\cos^2\theta}{\sin\theta}\]Ok good! From here we're going to split up the cosines on top,\[\large \frac{\cos^2\theta}{\sin\theta}\qquad=\qquad \frac{\cos \theta\cdot \cos \theta}{\sin \theta} \qquad=\qquad \frac{\cos \theta}{\sin \theta}\cdot \cos \theta\]

Answer 21

And from here we need to remember another identity.

\(\large \dfrac{\cos\theta}{\sin\theta}=?\)

Answer 22

cot theta