Question

Please help! Reduce (sin65degrees)/(1+cos65degrees) to a single function of one angle.
a. tan32degrees 30'
b. tan130degrees
c. cot32degrees 30'
d. cot130degrees

Answer 1

We have
\[\frac{\sin 65}{1+\cos 65}\]
@IloveCharlie what's cos 0?

Answer 2

@IloveCharlie are you here?

Answer 3

Oh yea, just a second

Answer 4

np

Answer 5

1?

Answer 6

Good so, I'll rewrite it as
\[\frac{\sin 65}{\cos 0+\cos 65}\]
Do you know what's \(\large \cos A+\cos B\)?

Answer 7

@IloveCharlie ???

Answer 8

No, I don't :(

Answer 9

NP
\[\large \cos A+\cos B=2\cos (\frac A2-\frac B2)\cos (\frac A 2+\frac B2)\]
so we get now
\[\large \frac{\sin 65}{2\cos (\frac 02-\frac {65}2)\cos (\frac 0 2+\frac {65}2)}\]
Do you get this?

Answer 10

Oh, yea, makes sense

Answer 11

good...would you tell me what's \(\sin 2\theta\) in terms of \(\sin \theta\ and\ \cos \theta\)?

Answer 12

@IloveCharlie ??

Answer 13

Uhhhh, ? No :(

Answer 14

it's given as
\[\sin 2\theta=2 \sin \theta \times \cos \theta\]
using this formula. we'll get
\[\large \frac{2\sin (\frac{65}{2})\times\cos(\frac{65}{2})}{2\cos (-\frac {65}2)\cos (\frac {65}2)}\]
what would we get now?

Answer 15

@IloveCharlie ??

Answer 16

K sorry, this keyboard isn't working. Just a second

Answer 17

cool:)

Answer 18

.9063/1.422 ? I'm thinking I did that wrong :/

Answer 19

don't compute the values, just simplify

Answer 20

sin(65)/1+cos(65) ?

Answer 21

nope, check again.
I think you have written the question again:)

Answer 22

:O I'm not sure :/

Answer 23

\[\large\large \frac{\cancel 2\sin (\frac{65}{2})\times\cancel{\cos(\frac{65}{2})}}{\cancel 2\cos (-\frac {65}2)\cancel{\cos (\frac {65}2)}}\]
what would you get now?

Answer 24

sin(65/2)/cos(-65/2)

Answer 25

@IloveCharlie what's
\[\large \cos (-x)\]
???

Answer 26

cos(x)?

Answer 27

good so we'll get now
\[\large \frac{\sin \frac{65}{2}}{\cos \frac{65}{2}}\]
now what would you get?

Answer 28

tan65/2?

Answer 29

yeah so it's
\[\tan 32.5 degrees\]
convert the 0.5 degrees into minutes

Answer 30

So a.! THANK YOU SO MUCH ASH!

Answer 31

you're welcome, did you understand?

Answer 32

Yes, thanks for explaining each step

Answer 33

np:D