Question

how to solve the equation of Cos2X+6Sin square X=4

Answer 1

\[ \cos(2x) + 6 \sin^2(x) = 4\]
?

Answer 2

I would use the double angle formula
see http://www.sosmath.com/trig/douangl/douangl.html
to put cos(2x) in terms of sin^2(x)

Answer 3

BUT WHAT IS THE VALUE OF x?

Answer 4

I CAN FIND COSX IS EQUAL TO + OR - SQUARE ROOT OF COS 2X +2 OVER 6 BUT I CAN'T DETERMINE THE VALUE OF (X)?

Answer 5

you need to change cos(2x) into a form with just sin^2(x)

can you do that ? see site posted above for the formula

Answer 6

ok I find sin square (X) IS EQUAL TO 1OVER 2 OR 1\2, THEN X IS EQUAL TO 30 DEGREES?

Answer 7

how. can you show your work?

Answer 8

Ok this the work, I change cos2x by cos square x plus sins square x and I have the complete equation : 1-sin square x + sin square x +6 sin square x =4 , and we have left 6 sins square x=4-1 then sin square =1\2

Answer 9

by looking for the value of the angle then I get X is equal to 30 degrees of sin square 1\2

Answer 10

Sorry sin square x = 1\2

Answer 11

notice
cos2x by cos square x plus sins square x

\[ \cos(2x) = \cos^2(x) - \sin^2(x) \]
if you use
\[ \cos^2(x) = 1 - \sin^2(x) \]
you can say
\[ \cos(2x) = 1 - 2\sin^2(x)\]

Answer 12

it is cos squared MINUS sin squared

Answer 13

ok thank you I went the other way I will correct it

Answer 14

now we have x is equal to 48,59 degrees?

Answer 15

but the sin square doesn't change the value of (x)?

Answer 16

can you show your work?

Answer 17

ok we have as equation :cos2x+6 sin square x =4, I replace cos2x by 1- 2sin square x + 6 sin square x=4. We have left: 4 sin square=4-1 ,then 4 sin square= 3 , we have at the end sin square x= 3\4 and I look for the value of the angle I have 48, 59 degrees in the calculator.?

Answer 18

looks ok until the last step
\[ \sin^2(x) = \frac{3}{4} \]
you want sin(x) not sin squared. take the square root of both sides
\[ \sqrt{\sin^2(x) }= \sqrt{\frac{3}{4} } \\
\sin(x) = \frac{\sqrt{3}}{2}
\]

Answer 19

it should probably be
\[ \sin(x) = ±\frac{\sqrt{3}}{2} \]

Answer 20

Ok I agree with you, I do want sin (x) not sin square (x).That is perfect, you are the best. Sometimes trig is very tricky.

Answer 21

you should get x= 60º , 120º, 240º, and 300º

Answer 22

but I can not get the those values in the calculator, x= root of 3 over 2 and I get error from the machine. I don't know how come this happens?

Answer 23

you should do inverse sin (look for the button labeled \(\sin^{-1}\) on sqr(3)/2

Answer 24

However, most people memorize certain angles and their sin, cos and tan
see
http://www.analyzemath.com/trigonometry/special_angles.html

Answer 25

thank you I do it by hand , I get root of 3 is equal to 1,74 and then I divide it by 2 from I get sinx is equal .86 and I find the angle of the first x which is equal to 59,31 degrees

Answer 26

you should do it with the calculator. first do sqr 3 =
then divide by 2
you should see 0.86....
then do inverse sin

Answer 27

yes this what I did

Answer 28

thank you very much