1 in terms of the other

[Timcago]

I do not understand how to work these problems.

Using the equation of the unit circle x^2 + y^2 = 1, find the following.

A) Write tant in terms of sint, where the terminal point determined by t is in quadrant II.

B) write cott in terms of sect, where the terminal point determined by t is in quadrant IV.

Heres what ive done so far

A) Change x to cost and y to sint

cos^2t + sin^2= 1

subtract sin^2t to both sides

Cos^2t = 1 - sin^2t

Take the sqaure root of both sides

Cost=+/- (1 - sin^2t)^(1/2)

Change Cost to tant by putting sint above it

Sint_________________Sint
----- = tant =+/- ----------------------
cost___________(1 - sin^2t)^(1/2)

So is this the answer?

______________Sint
tant = - ---------------------- (its negative because tant is neg in the 2nd quad)
________(1 - sin^2t)^(1/2)


B) I do not know how to do b, can someone show me the way?

 

[wjm11]

A) Write tant in terms of sint, where the terminal point determined by t is in quadrant II.

B) write cott in terms of sect, where the terminal point determined by t is in quadrant IV.

______________Sint
tant = - ---------------------- (its negative because tant is neg in the 2nd quad)
________(1 - sin^2t)^(1/2)

Hi, Tim,

Your solution to A) looks good. Use the same approach for B. Cotangent is the inverse of tangent, so cott = cost/sint, of course. Put the sint into terms of cost, once again using the Pythagorean identity, similarly to what you did in part A). Then turn the cosines into secants, since sect = 1/cost. And as before, keep track of your signs since you're in the 4th quadrant.

Hope that helps.

 

[Timcago]

thanks i think i got it

ended up with

_____________1
cott = - --------------------
_______(1-sec^2t)^(1/2)

 

[wjm11]

_____________1
cott = - --------------------
_______(1-sec^2t)^(1/2)

Pretty close. Your denominator needs to be switched around however. As it stands, you'll end up trying to take the square root of a negative number. The expression should be

cott = -1/((sect)^2-1)^(1/2)

It is always a good idea to check your work by plugging in a number you know the answer for.