Question

Fan and Medal!!!

Answer 1

simplify \[(1-\cos(\Theta)(1+\cos(\Theta)/(1-\sin(\Theta)(1+\sin(\Theta)\]

Answer 2

(1 - cos(theta))(1 + cos(theta))
--------------------------
(1 - sin(theta))(1 + sin(theta))

Answer 3

a. sin^2(theta)
b. cos^2(theta)
c. tan^2(theta)
d. cos(theta) / sin(theta)

Answer 4

Do you know how to multiply the numerator together? aka distribute the fraction

Answer 5

I have no clue when I comes to trig

Answer 6

this problem is the same as (2-x) (2+x) for example.
Do you know how to multiply this out? ^^^^^

Answer 7

yeah, 4 + 2x - 2x - x^2

Answer 8

-x^2 + 4

Answer 9

good now think, when cos(x) times cos(x) it becomes cos(x) squared , or we write as
cos^2x

Answer 10

1 + cos(theta) - cos(theta) - cos(theta)^2

Answer 11

-cos(theta)^2 + 1

Answer 12

-sin(theta)^2 + 1

Answer 13

d??

Answer 14

good! :)
just leave it as 1-cos^2 theta / 1-sin^2theta

then you know that
sin^2x + cos^2x = 1
1-cos^2x = sin^2x
1-sin^2x = cos^2x

Answer 15

not yet! Plug those in first. Not D :))

Answer 16

what do I plug them into??

Answer 17

you know that 1-cos^2theta = sin^2 theta, so replace the numerator of

1-cos^2 theta/1-sin^2 theta

with sin^2 theta

the we'd get


sin^2 theta/1-sin^2 theta

Answer 18

do you know the formular
sin^2 theta + cos^2 theta = 1? That's where we can use to plug in

Answer 19

so its now tan^2(theta)?? or sin^2(theta)?
I remember that formula

Answer 20

Yes! tan^2 theta!! Correct!

because sin^2 theta / cos^2 theta = tan^2 theta

sin/cos = tan

Answer 21

oh yeah!!! I got it from a previous lesson. thanks so much!!

Answer 22

\(\color{salmon}{\large\heartsuit}\large\text{You're Most Welcome! }\color{salmon}\heartsuit\)
\(~~~~~~~~~~~~~~~\color{green}{\large\ddot\smile}\color{blue}{\large\ddot\smile}\color{salmon}{\large\ddot\smile}\color{blue}{\large\ddot\smile}\color{salmon}{\large\ddot\smile}\)
\(~~~~~~~~~~~~~~~~~~~~\color{salmon}{\large\bigstar}\color{salmon}{\large\bigstar}\color{salmon}{\large\bigstar} \)

Answer 23

do u mind helping me out with another question please?

Answer 24

Yes, sure :)

Answer 25

thanks. one sec

Answer 26

The temperature of a chemical reaction ranges between 30°C and 70°C. The temperature is at its lowest point when t = 0 and completes one cycle over a 10-hour period. What is a sine function that would model this reaction?

Answer 27

a. f(t) = 20 sin 10t + 50
b. f(t) = 50 sin 10t + 20
c. f(t) = 50 sin pi/5t + 20
d. f(t) = 20 sin pi/5t + 50

Answer 28

I think its c but im not sure

Answer 29

Hm it's not C. Here's an easy way to think about this

Answer 30

what's sin of 0?

Answer 31

0

Answer 32

Quote (chemical reaction RANGES between 30°C and 70°C. The temperature is at its lowest point when t = 0 )

Let's say you think it's C.

f(0) = 0 + 20

It says range from 30 TO 70 . The equation MUST NOT go below 30 degrees. So C and the other answer with 20 degrees at the end is wrong.

Answer 33

So now you eliminate 2 answers. All that's left is to figure out the B value

Answer 34

i thought it couldn't be a or d. since the amplitude is 20?

Answer 35

wow im stupid sorry, your right thanks so much