Solving cot pi/4 and sec 5*pi/4

[garytse86]

There are two questions, I can solve the first one but not the second one with the same method.

find the exact value of cot pi/4 in surd form.

cot pi/4

= 1/ tan (pi/4)

= 1 / tan 45 ( in degrees)

= 1 / 1

= 1

which is the right answer according to the book.

However when I tried the next question - sec 5 * pi / 4, there are problems.

sec 5 * pi / 4

= 1 / cos (5 * pi / 4)

= 1 / cos (900/4) ( in degrees)

= 1/ cos(225)

and then I am stuck here. How do I express this in surd form?

The correct answer is minus(2^0.5)

and all I know is cos45 = 1/root2, cos30 = root3/2 and cos 60 = 0.5

Can someone help me get to the correct answer?

 

[garytse86]

sorry people I figured out the correct answer.

1 / cos225

= 1/ cos135

= 1/ cos(180-45)

= 1/ -cos45

= 1/ -1/root2

= minus root2

= - 2^0.5, which is the answer in the book.

 

[HallsofIvy]

Glad you got that straightened out. But I note that you always convert to degrees.

If you are going to continue in mathematics, you should learn to "think" in radians rather than degrees. In advanced mathematics, radians are the "default" measure for angles. (Actually, in advanced mathematics, sine, cosine, etc. are defined independently of angles and the independent variable has no units- to connect them with trig functions of angles you have to assume radians.) In this problem, did the book say "cot(pi/4) radians" or just "cot(pi/4")? If the latter, why did you assume radians? (You were right to do so, I'm just pointing out that you should understand WHY that is right.)

You shouldn't to convert to degrees, you should immediately think "sin(pi/4)= sqrt(2)/2, cos((pi)/4)= sqrt(2)/2" etc.

 

[garytse86]

I am not sure to be honest, but pi is always 180 degrees so I assumed it was in radians? If I am wrong can you please correct me. thanks a lot.

 

[STAii]

He didn't say that u are wrong.
He only adviced you to get used not to convert in radians.
For example, when you think 45^o, it means something to you, if you want to think in radian then pi/4 should means the same to you without converting it to degrees.
It is like if you know two languages, say english and french, and your native language is english (you learned french after english), then it is wrong to translate every french sentence you hear to english in order to understand it, you should understand it directly in french .