Solve: 2sinx = cosx?

Question

Please leave some clear working and solutions. Thanks.

Similar problem: cosx(sinx-cosx)=0

Answer 1

2 sin x / cos x = 1
2 tanx = 1
tan x = 1/2 (1st and 3rd quadrants)
x = 26.6° , 206.6°

cos x.(sinx - cos x) = 0
cos x = 0, sin x = cos x
cos x = 0 , tan x = 1
x = 90°, 270° , x = 45° , x = 225°

Answer 2

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2sinX * cosX - (√ 2) * cosX = 0 cosX { 2sinX - (√ 2) } = 0 cosX = 0 or sinX = (√ 2) / 2 X = π / 2 or X = π / 4 generalise

Answer 3

2sinx Cosx

Answer 4

Imagine a right-angled triangle with sides X,Y,Z where Z is the hypotenuse and X is opposite angle x. We now have :

sinx = X/Z so 2sinx = 2X/Z and cosx = Y/Z. So we have:

2X/Z = Y/Z. Dividing both sides by Z we get:

2X = Y. So tanx = X/2X (substituting 2X for Y)
Dividing by X we get: tanx = 1/2
Using a calculator we get:

tanx = 26.56 deg.

Sorry, I should also have mentioned that there would also be an answer in the third quadrant, as some people have quite correctly pointed out.

Answer 5

Divide both sides by cosX, you get 2SinX = sqrt 2 divide both sides by 2 SinX = (sqrt2)/2 SinX = 1/sqrt2 You know that Sin45 = 1/sqrt2 So you get X = 45 degrees or [(pi)/4 radians]

Answer 6

2sinx = cosx
===> 2sinx/cosx = 1
===> sinx/cosx = 1/2
===> Tan x = 0.5
Therefore, x = 26.57

Now you need to decide in which quadrant this angle lies.
Tangent is positive in 1st and 3rd quadrants. Therefore,
x = 26.57 or (180 + 26.57) = 206.57

Hope this helps.

Answer 7

Divide both sides by 2 cos x, remembering that
(sin x)/(cos x) = tan x, and so

tan x = 1/2

Using your calculator to find
arctan (1/2) [probably tan^(-1) (1/2) on your keyboard]
gives about 26 degrees, or, if your calculator is set in radians, probably about 0.4. Are you told what the domain of answers is? Because if you add any integer multiple of 180 degrees to the degree answer, or any integer multiple of pi to the radian answer, you get another valid solution. This is because the tangent is positive in the first and third quadrants.

PS I don't know any Mathematics teacher who would approve of putting "=" between the various equation lines as the second answerer has. You can say "therefore" or use an equivalence arrow, but don't say an equation is equal to an equation.

Answer 8

2sinx = cosx
sinx/cosx = 1/2
tanx = 1/2
x = 26.6, 180+26.6
x = 26.6, 206.6 (to 3 sig fig and assuming that 0

Answer 9

Your first question has been answered many times above, I'll tackle your second :-)

cos(x)(sin(x)-cos(x)) = 0

Divide by cos(x) :

sin(x) - cos(x) = 0

sin(x) = cos(x)

Divide by cos(x):

sin(x) / cos(x) = 1

sin(x) / cos(x) = tan(x)

tan(x) = 1

arctan(1) = x

x = 45 degrees ( or pi / 4 radians, Key angle, given by calculator)
OR
x = 225 degrees (5pi /4 radians, Worked out using the CAST diagram)

Answer 10

2sinx=cosx
then sinx/cosx=0.5 then tanx=0.5 so x=26.56 degrees(using calculator)