MHB How to Solve Trigonometric Equation sin2x = sqrt(2)/2 Using Algebra?

Click For Summary
To solve the equation sin(2x) = sqrt(2)/2 within the interval 0 to 2π, the initial solutions found are π/8 and 3π/8. The discussion clarifies that to find additional solutions, one can consider the periodic nature of the sine function. By adding 2π to the angles π/4 and 3π/4, the new solutions of 9π/8 and 11π/8 are derived. Dividing these by 2 confirms they fit within the specified interval. The approach effectively utilizes algebraic manipulation and the properties of trigonometric functions.
manish00333
Messages
2
Reaction score
0
Solve sin2x= sqrt(2)/2 (using algebra)
the interval is between 0 and 2pi

i got the first two answers: pi/8 and 3pi/8, but i don t understand how to get the other two: 9pi/8 and 11pi/8.

thanks!
 
Last edited:
Mathematics news on Phys.org
If we are told:

$$0\le x<2\pi$$

then:

$$0\le 2x<4\pi$$
 
Oh, that makes sense!

So, pi/4 + 2pi = 9pi/4
and 3pi/4 + 2pi = 11pi/4

and when i divide them by 2, i get 9pi/8 and 11pi/8.

thank you so much! :D
 
manish00333 said:
So, pi/4 + 2pi = 9pi/4
and 3pi/4 + 2pi = 11pi/4

and when i divide them by 2, i get 9pi/8 and 11pi/8.

Perfect! (Yes)
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
View full post »

Similar threads

MHB Finding Points of Intersection for Trigonometric Functions
  • · Replies 8 ·
Replies
8
Views
3K
MHB How to Solve the Trigonometric Equation 6*Sin^2(x) - 3*Sin^2(2x) + Cos^2(x) = 0?
  • · Replies 6 ·
Replies
6
Views
3K
High School Trigonometric equation -- real roots
  • · Replies 5 ·
Replies
5
Views
1K
Solving a trigonometric equation with multiples of ##\tan##
  • · Replies 7 ·
Replies
7
Views
2K
MHB DeMoivre's Theorem express (sqrt(2)/2 + sqrt(2)/2 i)^8 in a+bi form
  • · Replies 2 ·
Replies
2
Views
2K
High School What went wrong with (-x)^2=x^2?
  • · Replies 22 ·
Replies
22
Views
2K
MHB Equation 2: Prove that ##x^2+2x\sqrt x+3x+2\sqrt x+1=0##
  • · Replies 4 ·
Replies
4
Views
1K
MHB Solve Equation: $\sqrt{1+\sqrt{1-x^2}}$
  • · Replies 3 ·
Replies
3
Views
1K
Undergrad Simplifying a nested radical that includes a complex number
  • · Replies 5 ·
Replies
5
Views
2K
MHB How can I solve the trigonometric equation $(2-\sqrt{2})(1+\cos x)+\tan x=0$?
  • · Replies 6 ·
Replies
6
Views
3K