angle x is sin(2x) =-3/4 what is the exact value of cos (2x)?

Question

and what are the values of sin x and cos x

Answer 1

sin(2x) =-3/4 (ie 2x can be either in quadrant 3 0r in quadrant 4)

Now sin²(2x) + cos²(2x) = 1

So cos²2x = 1 - sin²(2x)
=1 - 9/16
= 7/16
Therefore cos(2x) = ±√(7)/4
(Note: 2x being in quadant 3 or quadrant 4 means sign of cos(2x) could be either + or -)

Answer 2

have to use cos^2+sin^2 =1
cos^2 (2x) = 1-sin^2 (2x)
= 1- (-3/4)^2
= 1-9/16 = 7/16
taking sq rt
cos (2x) = sq rt(7)/4

Answer 3

First determine cos(2x) from

sin^2 (2x) + cos^2 (2x) = 1

cos(2x) = sqrt(1-(-3/4)^2) = sqrt(1-9/16) = sqrt(7/16) = sqrt(7)/4

= 0.6614 or -0.6614

Now use the formula:

sin^2 x = (1-cos(2x))/2

so sin^2 x = (1- sqrt(7)/4)/2 = (4-sqrt(7))/8 = 0.16928

so sin x = sqrt(0.16928) = 0.4114 or -0.4114

And cosx =sqrt(1-sin^2 x) = sqrt(1-0.16928) = 0.9114 or -0.9114

OR sin^2 x = (4+sqrt(7))/8 = 0.8307

and sinx = sqrt(0.8307) = 0.9114 or -0.9114

And cosx =sqrt(1-sin^2 x) = sqrt(1-0.8307) = 0.4114 or -0.4114



Here's a useful trig identity link:

http://www.sosmath.com/trig/Trig5/trig5/trig5.htm

Answer 4

sin^2 (2x)+cos^2(2x)=1
(-3/4)^2+cos^2(2x)=1
cos^2(2x)=1-9/16 = 7/16
then
cos (2x) = +- sqrt(7)/4

Answer 5

sin(2x) = 2sin(x)cos(x) sin(x) = ?{a million - cos²(x)} sin(x) = ?{a million - (3/5)²} sin(x) = ?{a million - 9/25} sin(x) = ?{25/25 - 9/25} sin(x) = ?{sixteen/25} sin(x) = 4/5 sin(2x) = 2(4/5)(3/5) sin(2x) = 2(12/25) sin(2x) = 24/25

Answer 6

7/16

Answer 7

How about using:

sin2x + cos2x = 1?