Question (1 Viewer)

[Kutay]

This is the question i was wondering if what i have done is right

states.... P is a point where the graphs of y = tan@ and y = cos@ intersect

(i) x coordinate of P is a, show that sin@ = cos^2@ (DONE)
(ii) Prove that, at all such points P, the tangents to the two graphs are perpendicular
(THIS IS WHAT I DID)

well i stated for it to be perpindicular must incorporate the concept of m1 X m2 = -1
then i used the infomation used in the previous questions got stuck with like

sin# = cos2@ / 2 + 1/2

but stopped because not sure what i was doing is correct... can someone guide me in if i am on the right track or not ?

 

[noah]

at the point P: sin @ = cos^2 @ where @ is the x coordinate at P

y = tan x

y' = sec^2 x

at point P: sec^2 @ = sin^-1 @

(cos^2 @ = sec^2 @)

therefore m1 = sin^-1 @

y = cos @

y' = -sin @

therefore m2 = -sin @

m1 x m2 = sin^-1 @ x -sin @

= -1

therefore perpendicular

 

[Kutay]

thankyou ....