wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

The angle of intersection of curves. y = [|sin x| + |cos x|] and x2+y2=5 where [.] denotes greatest integral function is


A

π4

No worries! Weā€˜ve got your back. Try BYJUā€˜S free classes today!
B

tan1(12)

No worries! Weā€˜ve got your back. Try BYJUā€˜S free classes today!
C

tan1(2)

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D

none of these

No worries! Weā€˜ve got your back. Try BYJUā€˜S free classes today!
Open in App
Solution

The correct option is C

tan1(2)


We know that. 1|sin x|+|cos x|2
y=[|sin x|+|cos x|]=1
Let P and Q be the points of intersection of given curves.
Clearly, the given curves meet at points where y = 1 so, we get
x2+1=5x=±2

Now, P(2, 1) and Q(-2, 1)
Differentiating x2+y2=5 w.r.t. x, we get 2x +
2ydydx=0dydx=xy(dydx)(2.1)=2 and (dydx)(2.1)=2
Clearly the slope of line y = 1 is zero and the slope of the tangents at P and Q are (-2) and (2) respectively.
Thus, the angle of intersection is tan1(2)
Hence the correct option is c


flag
Suggest Corrections
thumbs-up
1
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Geometrical Interpretation of a Derivative
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon