3 unit Trig Questions from Year 12 Tetbook. (1 Viewer)

[big_bang344]

Can someone help me with a few trig questions from the Year 12 3 unit textbook? I need help with Exercise 2A Question 13 (a), (c) (f) and (h). I'll rep whoever that is able to help me Been stuck on these for quite a while :S

 

[bleakarcher]

can u give me the questions dude, or one by one at least?

 

[AAEldar]

Write the questions up preferably.

Plus you didn't specify which textbook.

 

[SpiralFlex]

There is only one textbook that has trigonometry in its second chapter. The Cambridge book. Unfortunately, I need to go so I can't answer your questions until tomorrow.

 

[bleakarcher]

I can get my hands on cambridge, one second (not literally).

 

[bleakarcher]

Can someone help me with a few trig questions from the Year 12 3 unit textbook? I need help with Exercise 2A Question 13 (a), (c) (f) and (h). I'll rep whoever that is able to help me Been stuck on these for quite a while :S

a) cot(2A)+tan(A)=cosec(2A)
Let t=tan(A)
Now, LHS=[(1-t^2)/2t]+t=[1-t^2+2t^2]/2t=(1+t^2)/2t=1/sin(2A)=cosec(2A)=RHS
:.cot(2A)+tan(A)=cosec(2A) as req.
c)sin(3A)/sin(A)+cos(3A)/cos(A)=4cos(2A)
Now, LHS=sin(A+2A)/sin(A)+cos(A+2A)/cos(A)=[sin(A)cos(2A)+sin(2A)cos(A)]/sin(A)+[cos(A)cos(A)-sin(A)sin(2A)]/cos(A)
ie LHS=[sin(A)[cos^2(A)-sin^2(A)]+2sin(A)cos^2(A)]/sin(A)+[cos(A)[cos^2(A)-sin^2(A)]-2sin^2(A)cos(A)]/cos(A)
ie LHS=cos^2(A)-sin^2(A)+2cos^2(A)+cos^2(A)-sin^2(A)-2sin^2(A)=4cos^2(A)-4sin^2(A)=4[cos^2(A)-sin^2(A)]=4cos(2A)=RHS
:.sin(3A)/sin(A)+cos(3A)/cos(A)=4cos(2A) as req.

 

[bleakarcher]

f) [1+sin(2A)]/[1+cos(2A)]=1/2[1+tan(A)]^2
Let t=tan(A)
Now, RHS=1/2[1+t]^2=1/2[1+2t+t^2]=[1+t^2+2t]/2
ie RHS=[[2t/(1+t^2)]+1]/[2/(1+t^2)]=[[2t/(1+t^2)]+1]/[(1+t^2+1-t^2)/(1+t^2)]
ie RHS=[[2t/(1+t^2)]+1]/[1+[(1-t^2)/(1+t^2)]=[1+sin(2A)]/[1+cos(2A)]=LHS
:.[1+sin(2A)]/[1+cos(2A)]=1/2[1+tan(A)]^2

 

[bleakarcher]

h) 8cos^4(x)=3+4cos(2x)+cos(4x)
Now, RHS=3+4[2cos^2(x)-1]+2cos^2(2x)-1=3+8cos^2(x)-4+2[2cos^2(x)-1]^2-1
ie RHS=3+8cos^2(x)-4+2[4cos^4(x)-4cos^2(x)+1]-1=3+8cos^2(x)-4+8cos^4(x)-8cos^2(x)+2-1=8cos^4(x)=LHS
:.LHS=RHS as req.

Rep...? lol

 

[big_bang344]

I repped you Thanks for that bleak. Kinda forgot to specify which textbook. Hehe. Silly me. Thanks anyways Spi.

 

[bleakarcher]

why do i still only have rep power 3? can someone explain?

 

[Shadowdude]

why do i still only have rep power 3?

Because you don't have a lot of reputation here, obviously.

 

[bleakarcher]

how do i?

 

[Shadowdude]

You make posts... and then people rep you for it if they're good. And then you accumulate it.

 

[bleakarcher]

and those bars on the top of our username represent...?

 

[Mature Lamb]

and those bars on the top of our username represent...?

How much rep you have

 

[bleakarcher]

so basically the bars are relative to the rep power?

 

[bleakarcher]

so basically the bars are relative to the rep power?

 

[Shadowdude]

Yes.

 

[Shadowdude]

Yes.

 

[bleakarcher]

oorite, thanks