# trig identities topic assessment (integral maths) Q2

have no clue how to do this question:

In this question you must show detailed reasoning.
The curves y=cos(x) and y=sin(x/2) meet at the point P. 0<x<[pi]
Find the coordinates of the point P

where do i even start?? 😭
(edited 3 weeks ago)
Original post by bobinabr23
have no clue how to do this question:

In this question you must show detailed reasoning.
The curves y=cos(x) and y=sin(x/2) meet at the point P. 0
Find the coordinates of the point P

where do i even start?? 😭

Either use the double angle identity (and solve for x/2) or use the half angle identity (and solve for x) or use the definition of cos in terms of sin of the complementary angle.
(edited 3 weeks ago)
Original post by mqb2766
Either use the double angle identity (and solve for x/2) or use the half angle identity (and solve for x) or use the definition of cos in terms of sin of the complementary angle.

okay .. so after using the half angle identity, i got:

sin(x/2) = 2[sin(x/4)cos(x/4)]

then i tried to make equal to cos(x)
2[sin(x/4)cos(x/4)] = cos(x)

then dividing by 2..
[sin(x/4)cos(x/4)]= 1/2 cos(x)

for some reason i felt like i should equate 1/2 to sin(1/6π)
[sin(x/4)cos(x/4)]= sin(1/6π)cos(x)

next i do not know what to do.. should i equate sin(x/4) to sin(1/6π)
or i thought about dividing both sides by sin(x/4)cos(x/4).
Original post by bobinabr23
okay .. so after using the half angle identity, i got:

sin(x/2) = 2[sin(x/4)cos(x/4)]

then i tried to make equal to cos(x)
2[sin(x/4)cos(x/4)] = cos(x)

then dividing by 2..
[sin(x/4)cos(x/4)]= 1/2 cos(x)

for some reason i felt like i should equate 1/2 to sin(1/6π)
[sin(x/4)cos(x/4)]= sin(1/6π)cos(x)

next i do not know what to do.. should i equate sin(x/4) to sin(1/6π)
or i thought about dividing both sides by sin(x/4)cos(x/4).

Using the half anlge identity sin(x/2) = +/-sqrt((1-cos(x))/2) so youd get a trig equation in cos(x).

Youve used the double angle identity and youd do that on the cos(x) term to end up with an equation in sin(x/2)

Arguably the simplest is to use the identity complementary angle identity
sin(A) = cos(90-A)
or vice versa, on either of the two terms and then reason about the angle. The "detailed reasoning" part of the question is a bit of a hint that there is a solution which can be spotted, but they want a properly explained solution.
(edited 3 weeks ago)
Original post by mqb2766
Using the half anlge identity sin(x/2) = +/-sqrt((1-cos(x))/2) so youd get a trig equation in cos(x).

Youve used the double angle identity and youd do that on the cos(x) term to end up with an equation in sin(x/2)

Arguably the simplest is to use the identity complementary angle identity
sin(A) = cos(90-A)
or vice versa, on either of the two terms and then reason about the angle. The "detailed reasoning" part of the question is a bit of a hint that there is a solution which can be spotted, but they want a properly explained solution.

thank u sm i got the answer now!!