Trig Quadrant Question: Solving for secx=-5.2, 0≤x≤2π

[Destrio]

Solve: secx=-5.2, 0≤x≤2π

I'm getting 2 answers:
1.76, 4.52

The answer key is telling me there is only one
1.76

How do I only get 1 answer from this?

Thanks,

 

[Destrio]

Evaluate: cot4.47

I'm getting .23 when i plug in: tan(1/4.47)

but the answer key says .25
am I doing something wrong?

thanks

 

[courtrigrad]

1. $$\sec x = -5.2, \; 0\leq x\leq 2\pi$$

$$\frac{1}{\cos x} = - 5.2$$

$$\cos x = -\frac{1}{5.2} =$$

$$\arccos(\cos x) = 1.76$$

$$x = 1.76$$2. $$\cot 4.47 = \frac{1}{\tan 4.47}$$ not $$\tan(\frac{1}{4.47})$$

 

[Destrio]

thanks, I see what I did wrong for #2

but, why doesn't #1 have 2 answers?

 

[riddlingminion]

Because the second answer is in quadrant 4, where cos is positive.

 

[lotrgreengrapes7926]

No, it's in the 3rd quadrant. There should be 2 solutions.

 

[VietDao29]

Yes, there should be 2 answers. Cheers. :)

 

[Destrio]

Alright
Thanks everyone