MHB Given value of cos(A) and quadrant of A, find sin(A) and tan(A)

  • Thread starter Thread starter DeusAbscondus
  • Start date Start date
  • Tags Tags
    Value
AI Thread Summary
Given that cos(A) = -1/4 and A is in the second quadrant, the calculations for sin(A) and tan(A) are discussed. The correct values derived are sin(A) = √15/4 and tan(A) = -√15, confirming that sin(A) is positive and tan(A) is negative in this quadrant. The textbook's answers of tan(A) = -1/√15 and sin(A) = 1/√15 are incorrect based on the calculations presented. The discussion concludes with agreement on the derived values, affirming the calculations are accurate.
DeusAbscondus
Messages
176
Reaction score
0
Hi folks,

$\text{ Here is the problem: }$

$\text{ Given that } cosA = -\frac{1}{4} \text{ and given that A }$

$\text{ is an angle between 90 and 180 degrees, then find: }$

a) $tanA$ and

b) $sinA$

$\text{Here is my working out: }$

$\text{1. Since A is in the second quadrant, then tanA will be negative and sinA will be}$

$\text{positive.}$

$\text{2. Given that }cosA=-\frac{1}{4}$

$\text{then } -1^2+x^{2}=4^{2}\ and \ x^{2}=15$

$\therefore x=\pm \sqrt{15}\ \text{ but the only real answer here is: }x=\sqrt{15}$

$\text{Now, since }x=\text{opp side, }$

$\text{ and } -1=\text{adjacent side}$

$\text{ then: a) }tanA=\frac{\sqrt{15}}{-1}$

$\text{and b) }sinA=\frac{\sqrt{15}}{4}$

$\text{If this is right, then my textbook is wrong, since it gives the answers: }$

a) $tanA=-\frac{1}{\sqrt{15}}$

b) $sinA=\frac{1}{\sqrt{15}}$

$\text{Who is right? }$

$\text{Thanks, as always, DeusAbscondus}$
 
Mathematics news on Phys.org
Re: basic trig problem

DeusAbscondus - Textbook: 1-0... congratulations!(Clapping)...

Kind regards

$\chi$ $\sigma$
 
Re: basic trig problem

I agree with you:

$$\sin(A)=\sqrt{1-\cos^2(A)}=\frac{\sqrt{15}}{4}$$

$$\tan(A)=\frac{\sin(A)}{\cos(A)}=-\sqrt{15}$$
 
Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
Thread 'Imaginary Pythagorus'
I posted this in the Lame Math thread, but it's got me thinking. Is there any validity to this? Or is it really just a mathematical trick? Naively, I see that i2 + plus 12 does equal zero2. But does this have a meaning? I know one can treat the imaginary number line as just another axis like the reals, but does that mean this does represent a triangle in the complex plane with a hypotenuse of length zero? Ibix offered a rendering of the diagram using what I assume is matrix* notation...
Back
Top