Trig Functions stuf (1 Viewer)

[velox]

Say if u have a question like 2sinx = root3

We just use the rules such as sin(180-x) = sin x to get the 2nd/subsequent values right?

 

[Slidey]

2sinx = root3
sinx=sqrt3/2
x=60 or 120.

ASTC
All positive in 1st quad
Sin positive in 2nd quad
Tan Positive in 3rd quad
Cos poisitive in 4th quad.

Fo 1st quad go x
2nd go 180-x
3rd 180+x
4th 360-x

 

[KFunk]

You can use the [All Stations To Central] quadrants thing or you could just imagine a sin graph (I assume you're talking about the second solution where 0 < x < 360&deg; ).

Sin(90-x)=cosx but I assume you meant sin(180-x)=sinx which does work.

So you get x = 60&deg;, 120&deg; otherwise you could just use a general form. Whatever works for you.

EDIT: Nice edit .

 

[velox]

oops post editted

So slide we only go in the quadrants for which the answer is positive? Im not after a specific solution just a general way to solve these types of questions cos i miss easy marks.

 

[Slidey]

yeah

If sinx=a
If a is negative then you go for quadrants 3 and 4, but if it is positive you go for quadrants 1 and 2.

EDIT: Nice edit .

Sorry. I did the a minute after I posted it (hence no edit message). Didn't realise you'd also posted in that time.

 

[velox]

thanks guys however i have another question

With the aid of a diagram, find the equivalent expressions for:

(a) cos ( 3pi/2 + x)

I couldn't do these last year and still cant =/

 

[KFunk]

You could use the ASTC quadrant thing for this I geuss but essentially:
cos( 3&pi;/2 + x)
= cos[2&pi; -(&pi;/2 -x)]
=cos(&pi;/2-x) since cos is positive in the fourth quadrant and cos(x) = cos(2&pi;-x)
=sinx

 

[velox]

oh sweet. thanks again

 

[Slidey]

Why does everybody use capital Pi?

 

[velox]

dunno? Anyway......sorry to be a bother, but i get sin/cos graphs they are easy but how would u sketch this?

y = 3tan 2x ? I know the sketch (graphamatica) but dont know how to get there....

 

[Slidey]

Learn the graph of y=tanx

Multiplying by 3 makes it steeper (unlike sin, cos the range is all R, so there's no effect there).

Multiplying the angle by 2 divides the period by 2. Normally the period is pi, but now it is pi/2

 

[velox]

period = n /2pi right?

 

[withoutaface]

T = 2pi/n

 

[KFunk]

Why does everybody use capital Pi?

That's what lower case pi comes out as for me . &pi; pi, &Pi; Pi (It looks like a small capital)

 

[velox]

more dumb questions

Solve graphically
sin 2x = 0.5x

Ive found the point of intersection which is around (2.5,1.8). So basically the sin2x bit is in radians, and the 0.5x is just normal?

 

[KFunk]

Yup, then geustimate, bisect intervals, use newton's method, whatever you need to do to get you estimation to the rigthnumber of d.p's.

 

[Slidey]

(2.5,1.8) lies on both:
y=x/2
y=sin2x

Yes, it is in radians for sin2x, otherwise it would make no sense. Just make sure you never do it in degrees.

 

[velox]

yep ok. So all of those types of questions with trig functions such as cos,sin, tan are to be done in radians. And ones which involve logs, are just normal stuff right?

 

[velox]

What about this, if u differentiate sec x, i get two answers one being:
sinx.sec^2x

And the other being:
tanx.secx

Which one is right?

 

[shafqat]

well they both are
the second form is the one given in the table of standard integrals