# Math Help - Trig Fundamental question

1. ## Trig Fundamental question

I have a sample question in my text it reads: Use the fundamental identities to find the exact values of the six trig functions of t given that cot(t) = 1/7 and cos(t) < 0.

I came up with the answers:
sin(t)=7/√50
cos(t)=-√50
tan(t)=7
csc(t)=√50/7
sec(t)=√50

The book gives the following answers:
sin(t)=-7√2/10
cos(t)=-√2/10
tan(t)=7
csc(t)=-5√2/7
cot(t)=1/7

I can't quite figure out how I got the answers I did (and that they are so different from the answers shown in the book). Can anyone help me clear this up?

2. Originally Posted by Chanda
I have a sample question in my text it reads: Use the fundamental identities to find the exact values of the six trig functions of t given that cot(t) = 1/7 and cos(t) < 0.

I came up with the answers:
sin(t)=7/√50
cos(t)=-√50
tan(t)=7
csc(t)=√50/7
sec(t)=√50

The book gives the following answers:
sin(t)=-7√2/10
cos(t)=-√2/10
tan(t)=7
csc(t)=-5√2/7
cot(t)=1/7

I can't quite figure out how I got the answers I did (and that they are so different from the answers shown in the book). Can anyone help me clear this up?
Hi Chanda,

Your book answers 'rationalized' the denominators. It is convention not to have radicals in the denominator of a fraction.

$\sin t = -\frac{7}{\sqrt{50}}=-\frac{7}{5\sqrt{2}}=-\frac{7}{5\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}}=-\frac{7\sqrt{2}}{10}$

See if you can fix 'em now.

3. ## Thanks!

I see now, thanks so much! That really helps