burhan101
Solve without a calculator
Delete
Share
This Question is Closed
burhan101
Best Response
You've already chosen the best response.
0
\[\[\huge 4\tan^2-\sec^2x=0\]\]
burhan101
Best Response
You've already chosen the best response.
0
0<x<2pi
burhan101
Best Response
You've already chosen the best response.
0
@UnkleRhaukus
UnkleRhaukus
Best Response
You've already chosen the best response.
1
\[4\tan^2 (x)-\sec^2 (x)=0\]
burhan101
Best Response
You've already chosen the best response.
0
yup
UnkleRhaukus
Best Response
You've already chosen the best response.
1
\[\tan(\theta)=\frac{\sin(\theta)}{\cos(\theta)}\]\[\sec(\theta)=\frac{1}{\cos(\theta)}\]
UnkleRhaukus
Best Response
You've already chosen the best response.
1
•take the sec term to the other side of the equation,
•substitute the above definitions into your equation,
•multiply by the denominator
•divide by 4
•take the sqrt of both sides ,
•take the inverse trig function to isolate x
UnkleRhaukus
Best Response
You've already chosen the best response.
1
tell me if you get stuck.
burhan101
Best Response
You've already chosen the best response.
0
\[4\frac{ \sin^2x }{ \cos^2x }-\frac{ 1 }{ \cos^2x }=0\]
burhan101
Best Response
You've already chosen the best response.
0
what do i do next
UnkleRhaukus
Best Response
You've already chosen the best response.
1
multiply by cos^2
burhan101
Best Response
You've already chosen the best response.
0
to subtract the two ??
burhan101
Best Response
You've already chosen the best response.
0
(2sinx+1)(2sinx-1) / cos^2x
UnkleRhaukus
Best Response
You've already chosen the best response.
1
how did that happen?
burhan101
Best Response
You've already chosen the best response.
0
idk im guessing :S
UnkleRhaukus
Best Response
You've already chosen the best response.
1
start again and follow the •'s
burhan101
Best Response
You've already chosen the best response.
0
okay
burhan101
Best Response
You've already chosen the best response.
0
i'm going to be honest, im confused
burhan101
Best Response
You've already chosen the best response.
0
by following the checlist this is what im getting sinxcosx-sinx
Hero
Best Response
You've already chosen the best response.
2
May I suggest another approach?
UnkleRhaukus
Best Response
You've already chosen the best response.
1
...
burhan101
Best Response
You've already chosen the best response.
0
my teacher has a completely different way im confuseeed
UnkleRhaukus
Best Response
You've already chosen the best response.
1
well im sure there are many different ways ,
burhan101
Best Response
You've already chosen the best response.
0
Yahoo!
Best Response
You've already chosen the best response.
0
1 + tan^2 x = sec^2 x
tan^2 x = sec^2 x - 1
UnkleRhaukus
Best Response
You've already chosen the best response.
1
i dont like that way as much as i like the way i have outlined , but that is opinion
Yahoo!
Best Response
You've already chosen the best response.
0
4 ( sec^2 x - 1) - sec^2 x = 0
4 sec^2 x - 4 - sec^2 x = 0
3 sec^2 x = 4
sec x = 2/ sqrt (3)
burhan101
Best Response
You've already chosen the best response.
0
i am only allowed to have cos and sin in my answers
Yahoo!
Best Response
You've already chosen the best response.
0
Lol.....u shuld have Mentioned that in the question...)
burhan101
Best Response
You've already chosen the best response.
0
Steps:
1. rearrange and isolate the unknown
2. move everything to one since, set equal to zero
3. use the zero principle
4. use inverse trig to find the angle
5. use CAST or ASTC to adjust answers
@Yahoo! i know sorry ! :$
Hero
Best Response
You've already chosen the best response.
2
|dw:1355392376220:dw|
burhan101
Best Response
You've already chosen the best response.
0
guys I GOT IT ! :D
burhan101
Best Response
You've already chosen the best response.
0
i just used my teachers method but everyone's explanations helped.
thankyou :D
Hero
Best Response
You've already chosen the best response.
2
And what exactly was your teacher's method?
burhan101
Best Response
You've already chosen the best response.
0
we're supposed to find what x can and cannot equal
burhan101
Best Response
You've already chosen the best response.
0
so i just used basic trig and then looking at the unit circle i did elimination and listed the factors
Hero
Best Response
You've already chosen the best response.
2
That's not what you posted at the beginning
burhan101
Best Response
You've already chosen the best response.
0
burhan101 0
Steps:
1. rearrange and isolate the unknown
2. move everything to one since, set equal to zero
3. use the zero principle
4. use inverse trig to find the angle
5. use CAST or ASTC to adjust answers
burhan101
Best Response
You've already chosen the best response.
0
thats what i did, using the zero principle :
Hero
Best Response
You've already chosen the best response.
2
You mind showing some of those steps using the drawing button like I did?
burhan101
Best Response
You've already chosen the best response.
0
|dw:1355393054138:dw|
Hero
Best Response
You've already chosen the best response.
2
Kill your teacher bro
UnkleRhaukus
Best Response
You've already chosen the best response.
1
\[4\tan^2 (x)-\sec^2 (x)=0\]\[4\tan^2 (x)=\sec^2 (x)\]\[4\left(\frac{\sin(x)}{\cos (x)}\right)^2 =\left(\frac1{\cos(x)}\right)^2\]\[4\frac{\sin^2(x)}{\cos^2 (x)} =\left(\frac1{\cos^2(x)}\right)\]\[4\sin^2(x)=\frac{\cos^2(x)}{\cos^2(x)}\]\[4\sin^2(x) =1\]\[\sin^2(x) =\frac14\]\[\sin(x)=\frac 12\]\[x=\arcsin\left(\frac12\right)=60°\]
Hero
Best Response
You've already chosen the best response.
2
@UnkleRhaukus, you ignore negative values?
UsukiDoll
Best Response
You've already chosen the best response.
0
wow Hero that's just harsh, but...yeah..no comment
UsukiDoll
Best Response
You've already chosen the best response.
0
I'm not saying it sucks or anything though
RolyPoly
Best Response
You've already chosen the best response.
1
\[4\tan^2 (x)-\sec^2 (x)=0\]\[4\tan^2 (x)-(1+tan^2x)=0\]\[3\tan^2 (x)-1=0\]\[tan^2x = \frac{1}{3}\]That shouldn't be difficult.
RolyPoly
Best Response
You've already chosen the best response.
1
Just use the identity \(1+tan^2x=sec^2x\)
UnkleRhaukus
Best Response
You've already chosen the best response.
1
@hero
0<x<2pi
stated in question
Hero
Best Response
You've already chosen the best response.
2
I didn't see that second line. He posted it in pieces.