Trig help! (1 Viewer)

[JasonNg]

How do i solve this equation for x: sin2x = cosx

So confused...

 

[nightweaver066]

How do i solve this equation for x: sin2x = cosx

So confused...

Double angle formula:





You can do the rest yourself.

 

[deswa1]

Use double angles and factorise...



And then solve for the relevant domain. Good luck

Edit: Beaten

 

[JasonNg]

But we haven't learnt that method at Harry's yet. So we have to use a different method. :S

 

[deswa1]

What other method?

 

[JasonNg]

I'm don't know. All we've learnt is the 2-unit stuff without the formulae stuff.

 

[JasonNg]

Can you guys help me with this instead. Solve for x, 2 sec^2x = 5tanx

 

[Deliriously]

use complementary angles
sin2x = cosx
cos(90-2x) = cos(x)
etc

 

[CrackerMo]

Sorry to chime, but I also have a trig Q I am struggling with.

Solve sinx + cosx = cos2x using the auxiliary method.

Thanks TS and everyone else

 

[Carrotsticks]

Sorry to chime, but I also have a trig Q I am struggling with.

Solve sinx + cosx = cos2x for 0<x<2pi using the auxiliary method.

Thanks TS and everyone else

Have you learnt compound angle formulae yet, or perhaps Auxiliary angle expressions?

 

[CrackerMo]

Yep

 

[Drongoski]

Are all these trig questions homework from Harry's?

 

[CrackerMo]

Are all these trig questions homework from Harry's?

Sorry, mine was just from the Cambridge Year 12 3unit text, not from Harry's. Sorry for chiming!

 

[such_such]

Can you guys help me with this instead. Solve for x, 2 sec^2x = 5tanx

Using cross method...


and you can do the rest

 

[RivalryofTroll]

Using cross method...


and you can do the rest

This.
Note that:
sec^2x - tan^2x = 1
So sec^2x = 1 + tan^2x

 

[RealiseNothing]

Method 1)

sin2x = cosx

2sinxcosx= cosx

Divide both sides by cosx

2sinx = 1

sinx = 1/2

x = 30 or 150 degrees.



Method 2)

We know that sin(y) and cos(x) are equal if x+y=90

Since sin2x = cosx, we can see that 2x+x=90 (just imagine 2x being y)

Hence 3x = 90 and x = 30

But x can also equal 150 using sin(180-x) = sinx

 

[JasonNg]

Repped you guys! Can you guys show me how to do this last one? Solve for x,

6 tan^2x - 4sin^2x = 1

Thanks!

 

[Peeik]

Method 1)

sin2x = cosx

2sinxcosx= cosx

Divide both sides by cosx

2sinx = 1

sinx = 1/2

x = 30 or 150 degrees.

DO NOT DIVIDE ANYTHING....if you do you will overlook some solutions. Instead move over all the terms to one side then factorise.

2sinxcosx= cosx
2sinxcosx - cosx = 0
cosx(2sinx-1)=0
cosx=0 or sinx=1/2
x=90,270 or x= 30,150

Notice how you dont have the answers x=90,270?

 

[nightweaver066]

lol made a mistake wait

 

[Carrotsticks]

Haha nightweaver, how did you manage to get the upside down question mark?