Homework Help

If  `csc theta = sqrt(u^2+169)/u ` , find the expresion for `cot theta`  and `sec...

user profile pic

user354582 | (Level 1) Honors

Posted June 23, 2013 at 7:33 AM via web

dislike 1 like

If  `csc theta = sqrt(u^2+169)/u ` ,

find the expresion for `cot theta`  and `sec theta` .

1 Answer | Add Yours

user profile pic

mjripalda | High School Teacher | (Level 1) Senior Educator

Posted June 23, 2013 at 8:53 AM (Answer #1)

dislike 1 like

`csc theta =sqrt(u^2+169)/u`

To determine the expression for cotangent and secant, draw the corresponding right triangle of the given cosecant function. To do so, apply its formula which is:

`csc theta= (hypoten u se)/(opposite)`

So, the hypotenuse of the right triangle is `sqrt(u^2+169)` and the side opposite to angle theta is u. 

To determine the side adjacent to theta, apply the Pythagorean formula which is:


Plug-in c=sqrt(u^2+169)  and b=u.







Hence, the adjacent side is 13.

Now that the three sides of the triangles are known (refer figure below), expression for cotangent and secant can now be determined.

For cotangent, apply its formula which is the ratio of adjacent side to the opposite side of theta.

`cot theta = (adjacent)/(opposite)`

`cot theta = 13/u`

And for secant, it is the ration of hypotenuse to adjacent side of angle theta.

`sec theta=(hypoten u se)/(adjacent)`

`sec theta=sqrt(u^2+169)/13`



`cot theta = 13/u `       and       `sec theta=sqrt(u^2+169)/13`

This image has been Flagged as inappropriate Click to unflag
Image (1 of 1)

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes