Question

trig help!
solve each equation for solutions in the interval [0,2π) by first solving for the trigonometric function.
sec^2 x + 2 = -1

OR

(cotx - 1)(√3 cotx + 1) = 0

i'm stuck on both.. please help. any explanations are welcome..

Answer 1

for the second question, i set each to 0 and i got cotx = 1 and cot x = -1/√3
but i'm not sure what the next step is...
the answers in the back of the book are π/4, 2π/3, 5π/4, and 5π/3

Answer 2

Consider\[\cot x = 1\]Multiply both sides by tanx\[1=\tan x\]What value of x would tanx be 1?

Answer 3

π/4?

Answer 4

Yes! One more

Answer 5

that's the problem.. i only know how to find the first answer. i don't know how to find the second one :(
do i add 2π?

Answer 6

Note than tanx = tan(π+ x)

Answer 7

so π/4 + 2π?
9π/4?
i'm sorry.. i don't know what you mean..

Answer 8

No :(
Do you know that tan(π+x) = tanx?

Answer 9

no.. wait i think so. do you mean that the two angles are the same? like 45 and 225 degrees?

Answer 10

The two angles are NOT the same, BUT tan(45) = tan(225) :)

Answer 11

oh. then what do you mean by tan(π+x) = tanx? i've never heard of it..

Answer 12

pi = 180 degrees.
Let say, we have x = 45
tan(45) = tan(180+45) = 1
tan(180+45) is the same as tan(225).
Got it?

Answer 13

OH. yes i get it :D
so essentially the two angles are the same right? so i could add 180 to 45 as many times as i want and the two angles would still be alike?

Answer 14

For tan, yes.
That is tan(x) = tan(nπ +x)

Answer 15

okay thank you! :)
i think i know what i've been doing wrong. to find other angles, i've been adding 360(2π) instead of 180(π).
so back to my question.. i would solve for cotx and graph it. the first answer is π/4, and i would add π to get the second answer, right?

Answer 16

Yes.

Answer 17

So, the answers to (cot-1)=0 are...??

Answer 18

π/4 and 5π/4?

Answer 19

Yes

Answer 20

thanks so much ! :D

Answer 21

Now, can you solve √3 cotx + 1 =0?

Answer 22

√3 cotx + 1 =0
√3 cotx = -1
cotx = -1/√3
did i draw it right?