SOLUTION: Find all t in the interval [0, 2π] satisfying sin x − cos x = 1.
Algebra.Com
Question 476635: Find all t in the interval [0, 2π] satisfying sin x − cos x = 1.
Found 2 solutions by stanbon, Alan3354:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Find all t in the interval [0, 2π] satisfying sin x − cos x = 1.
---
Square both sides to get:
sin^2 - 2sin*cos + cos^2 = 1
----
Since sin^2+cos^2 = 1 you get:
-2sin*cos = 0
sin*cos = 0
Either sin(x) or cos(x) = 0
sin(x) = 0 when x = 0 or pi or 2pi
cos(x) = 0 when x = pi/2 or (3/2)pi
=====================================
Cheers,
Stan H.
===========
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
sin(x) - cos(x) = 1
-------------------
sin - sqrt(1 - sin^2) = 1
Sub x for sin(x)
x = 1 + sqrt(1 - x^2)
x-1 = sqrt(1 - x^2)
x^2 - 2x + 1 = 1 - x^2
2x^2 - 2x = 0
x = 0, x = 1
--------------
sin(x) = 0 or 1
--> x = 0, x = pi/4
RELATED QUESTIONS
Find all t in the interval [0, 2π] satisfying 2(sin t)2 − sin t =... (answered by Tatiana_Stebko)
1) Find all t in the interval [0, 2π] satisfying 2(sin t)2 − 3 sin t + 1 = 0
(answered by josgarithmetic)
Find all t in the interval [0, 2π] satisfying (cos t)2 − 6 cos t + 5 =... (answered by lwsshak3)
Find all t in the interval [0, 2π] satisfying (cos t)2 + 10 cos t + 9 = 0. (answered by lwsshak3)
Find all t in the interval [0, 2π] satisfying (cos t)2 + 4 cos t + 3 = 0.
(answered by lwsshak3)
Find all values of t in the interval [o,2π] satisfying sin(2t)=-1/2
(answered by Alan3354)
Find all solutions of the equation in the interval [0, 2π)
sin(x + π/4)... (answered by lwsshak3)
Find all solutions of the equation in the interval [0, 2π).
2 sin x/2 + 2 cos x =... (answered by lwsshak3)
Find all values of x in the interval [0, 2π] that satisfy the given equation.... (answered by Fombitz)