Question

If cos2 x + 2cosx - 2 = 0, then cosx = _____.

Answer 1

cos²x+2cosx-2=0 , like this ?

Answer 2

yes

Answer 3

oh my bad

Answer 4

in this case its still a quadratic though.

Answer 5

Okay, so \(\normalsize\color{blue}{ \cos^2 x + 2\cos x - 2 = 0}\) :)

For better vision let cos(x)=a, you come out with, \(\normalsize\color{blue}{ a^2 + 2a - 2 = 0}\)

lets complete the square.
\(\normalsize\color{blue}{ a^2 + 2a - 2 = 0}\)
\(\normalsize\color{blue}{ a^2 + 2a +1 = 3}\)
\(\normalsize\color{blue}{ (a+1)^2= 3}\)
\(\normalsize\color{blue}{ a= -1±\sqrt{3}}\)

Answer 6

oh!!! thank you!!

Answer 7

yes phys, it is just a quadratic, technically, besides that for 'a' we can have 1 or 2 solutions, and for cosine function there are infinite number of solutions in many different intervals.

Answer 8

You welcome, @garcia22and

Answer 9

could you help me with another problem? please

Answer 10

yes, perhaps.

Answer 11

In triangle ABC, a = 12, angleB = 25°, and angleC = 45°. Find b.

Answer 12

sin(110)/12 = sin(25)/b

Answer 13

I mean
A) 5.4
B) 6.6
C) 7.2
D) 22

Answer 14

No phys, angle A is not given yet, although, \(\normalsize\color{blue}{ ∠~A~~=~~180-(~~~∠~B + ∠~C~~)}\) .

Answer 15

You can't use the sine law yet, but after you find angle a, please go for it.

Answer 16

Sin(A)/a = Sin(B)/b = Sin(C)/c

Answer 17

so you solve for angle A. 180-25-45 = ?

Answer 18

\[\frac{ \sin110 }{ 12 }= \frac{ sinB }{ b }\]

Answer 19

right and we have Sin B

Answer 20

yes, we have the angle B, it is 25

Answer 21

when I get here what do I do next\[bsin110=5.071\]

Answer 22

to make it simpler you could just say 12sin(25)/sin(110) = B

Answer 23

I divide sin110?

Answer 24

think about it algebraicly

Answer 25

we want to isolate B

Answer 26

ok I got it, thanks!

Answer 27

Answer is 5.4

Answer 28

yep

Answer 29

cool!! another problem: Which of the following functions has a period of 4π ?

A) y = sinx
B) y = sinx
C) y = sin2x
D) y = sin4x

I thought it was B

Answer 30

so for sin functions the period = 2pi/B

Answer 31

uh for answers a and b are the same?

Answer 32

oh sorry A is y=sin1/4x and B is sin1/2x

Answer 33

2pi/B = 4pi (period) solve for B get 1/2, so the answer is sin1/2x

Answer 34

ah okay so I was right, cool!

Answer 35

The vertical component of a force of 100 pounds that makes an angle of 30° with the horizontal is 50 pounds. Is this true?