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

Click For Summary
SUMMARY

The discussion focuses on solving the trigonometric equation sin(2x) = √(2)/2 within the interval [0, 2π]. The initial solutions identified are π/8 and 3π/8. The participants clarify that to find additional solutions, one must consider the periodic nature of the sine function, leading to the solutions 9π/8 and 11π/8 by adding 2π to the angles π/4 and 3π/4, respectively, and then dividing by 2.

PREREQUISITES
  • Understanding of trigonometric functions and their properties
  • Knowledge of the unit circle and angle measures
  • Familiarity with algebraic manipulation of equations
  • Concept of periodicity in trigonometric functions
NEXT STEPS
  • Study the periodic properties of the sine function
  • Learn how to solve trigonometric equations using algebraic methods
  • Explore the unit circle and its application in trigonometry
  • Investigate the use of inverse trigonometric functions
USEFUL FOR

Students studying trigonometry, educators teaching algebraic methods for solving equations, and anyone looking to deepen their understanding of trigonometric identities and solutions.

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)
 

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
MHB DeMoivre's Theorem express (sqrt(2)/2 + sqrt(2)/2 i)^8 in a+bi form
  • · Replies 2 ·
Replies
2
Views
2K
Solving a trigonometric equation with multiples of ##\tan##
  • · Replies 7 ·
Replies
7
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
2K
MHB Solve Equation: $\sqrt{1+\sqrt{1-x^2}}$
  • · Replies 3 ·
Replies
3
Views
1K
MHB How can I solve the trigonometric equation $(2-\sqrt{2})(1+\cos x)+\tan x=0$?
  • · Replies 6 ·
Replies
6
Views
3K
MHB Solve the trigonometric equation?
  • · Replies 3 ·
Replies
3
Views
3K