Question

Pre-calculus/Trig help

Answer 1

Y = 2x^3 + 4x^2 + -5x + 3 Points: (1,-2)
Y = 2*1^3 + 4*-2^2 + (-5*1) + 3
Y = 2 + 16 + (-5) + 3
Y = 18 - 5 + 3
Y = 13 + 3
Y = 16 .... My guess on how you do it. Idk 100%

Answer 2

Lol i put the wrong attachment first XD

Answer 3

You changed the question =.= lol :/

Answer 4

Well I'm lost on that one.. that sign in the end, its pi? 3.1416 ? Normally used 3.14
On the previous.. am I right?

Answer 5

yes

Answer 6

@agent0smith @Hero

Answer 7

haha yip that's pi :D

Answer 8

If you want you can try and tag @math&ing001 <- smart :3

Answer 9

First, you set each individual trig function equal to zero, and get them alone, for, you know that if one of them is zero, then, since you're multiplying, they'll both be zero:\[\tan \theta -1 =0\rightarrow \tan \theta = 1\]\[\tan3* \theta = 0\]
Tan=1 when cos/sin=1...which is when they're both the same value, which is only at the pi/4's. Since the one has to be positive, you must divide -/- or +/+. This happens at pi/4 and 5pi/4.
Now, when tan=0; sin/cos=0, which happens when the numerator is 0, so 0/cos.
Sin is zero at 0 and pi, and (2pi is not in the interval).
Since the theta is being multiplied by 3, to counter act that, we divide the theta by 3:
sin3*pi, now its sin3(pi/3)=sin(pi)=0. They both hold true, so we just added another point in which the result would be 0.
Total: pi/4, 5pi/4, 0, pi, and pi/3. (I think you can say 2pi/3, but not too sure).

Answer 10

Oh my God thank you so Much @JonnyVonny

Answer 11

It can be 2pi/3, but can it be 3pi/2? @JonnyVonny

Answer 12

@hartnn

Answer 13

Well, 3*3=9, so that would be 9pi/2, which is when cos=0, taking it undefined.

Answer 14

making it*...therefore no lol

Answer 15

do you know how to find the general solution for these? @JonnyVonny

Answer 16

General solution for what? Sorry I'm late on typing; trying to rap >.>

Answer 17

Oh, in the question, 1 sec.

Answer 18

I think there are 2 general solutions in this, one for each in the parenthesis, which would be (pi+k*pi)/4 and the other one I'm not too sure about, want elaboration?

Answer 19

@ganeshie8

Answer 20

@ganeshie8 this one

Answer 21

yu want the general solution ?

Answer 22

yes

Answer 23

and were the specific solutions johnny gave right?

Answer 24

\(\tan 3x= 0\) or \( \tan x = 1\)

\(3x= \tan^{-1} 0\) or \( x = \tan^{-1}1\)

\(3x= n\pi + 0 \) or \( x = n\pi + \frac{\pi}{4}\)

\(x= \frac{n\pi}{3} \) or \( x = n\pi + \frac{\pi}{4}\)

above both are general solutions.

Answer 25

yes, they're absolutely correct.

Answer 26

we can get the specific solutions form general solution very easily
lets do it quick ?

Answer 27

yes

Answer 28

for the First general solution : \(\large x = \frac{n \pi}{3}\)
specific solutions are : \(\large x = \frac{0* \pi}{3}, \frac{1* \pi}{3}, \frac{2* \pi}{3}, \frac{3* \pi}{3}, \frac{4* \pi}{3}, \frac{5* \pi}{3}\)

Answer 29

simplify the fractions ok

Answer 30

0, pi/3, 2pi/3, pi,4pi/3, and 5pi/3

Answer 31

Yes, similarly find specific solutions from second general solution also

Answer 32

x=npi+pi/4 x=1pi+pi/4 x=2pi/4

Answer 33

try again

Answer 34

pi + pi/4 \(\ne\) 2pi/4

Answer 35

For the second general solution : \(\large x = n\pi+\frac{\pi}{4}\)
specific solutions are : \(\large x = 0*\pi + \frac{\pi}{4}, ~ 1*\pi + \frac{\pi}{4}\)

Answer 36

simplify and append these solutions to ur first set :) easy ok

Answer 37

idk how to simplify 1*pi+pi/4 :/

Answer 38

\(\huge \pi + \frac{\pi}{4}\)

Answer 39

to add fraction, we need to have SAME number in the bottom ok

Answer 40

so, multiply first term wid 4/4

Answer 41

\(\huge \pi + \frac{\pi}{4}\)

\(\huge \frac{4}{4} * \pi + \frac{\pi}{4}\)

Answer 42

now that bottoms are same, u can add tops

Answer 43

\(\huge \pi + \frac{\pi}{4}\)


\(\huge \frac{4}{4} * \pi + \frac{\pi}{4}\)


\(\huge \frac{4\pi + \pi}{4} \)

Answer 44

5pi/4 and for 0pi+pi/4 would it be pi/4?

Answer 45

and are there any other solutions @ganeshie8

Answer 46

yup ! oly those.

if u put n = 2, u wud get :-
2pi + pi/4

which is 2pi + something
clearly greater than 2pi

but we're asked to find specific solution oly within [0, 2pi)

so we're done. oly two solutions :- pi/4 and 5pi/4

Answer 47

thank you!

Answer 48

add them to the first set of solutions u got earlier

Answer 49

np :)
so in total you're getting 8 specific solutions hmm

Answer 50

x=0,pi/3,2pi/3,pi,4pi/3,5pi/3,5pi/4 and pi/4

Answer 51

looks good :)