+0  
 
0
482
1
avatar

2 cos x= sin x+1

Guest Nov 4, 2014

Best Answer 

 #1
avatar+27042 
+5

Square both sides:

4cos2x = sin2x + 2sinx + 1

 

Replace cos2 by 1 - sin2

4(1 - sin2x) = sin2x + 2sinx + 1

 

Collect terms

5sin2x + 2sinx - 3 = 0

 

This can be written as

(sinx + 5/5)(sinx - 3/5) = 0  or (sinx + 1)(sinx - 3/5) = 0

 

So sinx = -1 and sinx = 3/5

This means x = asin(-1) = 3pi/2 (=270°)

and x = asin(3/5) ≈ 36.87°

 

Adding and subtracting multiples of 2pi (360°) to these also satisfies the original equation.

.

Alan  Nov 4, 2014
 #1
avatar+27042 
+5
Best Answer

Square both sides:

4cos2x = sin2x + 2sinx + 1

 

Replace cos2 by 1 - sin2

4(1 - sin2x) = sin2x + 2sinx + 1

 

Collect terms

5sin2x + 2sinx - 3 = 0

 

This can be written as

(sinx + 5/5)(sinx - 3/5) = 0  or (sinx + 1)(sinx - 3/5) = 0

 

So sinx = -1 and sinx = 3/5

This means x = asin(-1) = 3pi/2 (=270°)

and x = asin(3/5) ≈ 36.87°

 

Adding and subtracting multiples of 2pi (360°) to these also satisfies the original equation.

.

Alan  Nov 4, 2014

23 Online Users

avatar
avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.