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

AI Thread 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 'Trigonometry problem of interest'

Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
View full post »
Thread 'Unit Circle Double Angle Derivations'

Thread 'Unit Circle Double Angle Derivations'

Here I made a terrible mistake of assuming this to be an equilateral triangle and set 2sinx=1 => x=pi/6. Although this did derive the double angle formulas it also led into a terrible mess trying to find all the combinations of sides. I must have been tired and just assumed 6x=180 and 2sinx=1. By that time, I was so mindset that I nearly scolded a person for even saying 90-x. I wonder if this is a case of biased observation that seeks to dis credit me like Jesus of Nazareth since in reality...
View full post »

Thread 'Fermat's Last Theorem'

Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
View full post »

Similar threads

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

Hot Threads

Recent Insights

Back
Top