Where cos(x) intersects sin(x)

  • Thread starter Thread starter alpha01
  • Start date Start date
Click For Summary
SUMMARY

The intersection points of cos(x) and sin(x) occur where cos(x) = sin(x). This can be expressed as tan(x) = 1, leading to the solution x = π/4 within the interval 0 < x < π/2. The corresponding y-coordinate at this intersection is y = sin(π/4) = cos(π/4) = √2/2. Therefore, the intersection point is (π/4, √2/2).

PREREQUISITES
  • Understanding of trigonometric functions: sine and cosine
  • Knowledge of the tangent function and its properties
  • Familiarity with solving equations involving trigonometric identities
  • Basic concepts of right-angled triangles
NEXT STEPS
  • Study the unit circle and its relation to trigonometric functions
  • Explore the properties of the tangent function and its graph
  • Learn about solving trigonometric equations in different intervals
  • Investigate the applications of trigonometric intersections in real-world scenarios
USEFUL FOR

Students of mathematics, educators teaching trigonometry, and anyone interested in understanding the relationships between trigonometric functions.

alpha01
Messages
77
Reaction score
0
we know that cos(x) intersects sin(x) in the interval 0< x< pi/2... but how can i find (x,y) points of this intersection? (without plotting and estimating based of the resultant graph)
 
Physics news on Phys.org
If cos(x)= sin(x) then sin(x)/cos(x)= tan(x)= 1. Solve that equation.
 
In a right angled triangle with hypotenuse of length 1 and one angle x, the side next that angle is cos x, the side opposite ... need I say more?
 

Similar threads

  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 40 ·
2
Replies
40
Views
5K
  • · Replies 3 ·
Replies
3
Views
2K
Replies
3
Views
2K
Replies
5
Views
2K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 6 ·
Replies
6
Views
2K
  • · Replies 20 ·
Replies
20
Views
2K
  • · Replies 14 ·
Replies
14
Views
2K