parametric eq question

Hello, I am currently trying to learn parametric equations and I'm confused about the method for this question. I did 0=1/4sint to get pi but the MS states to equal tcost=0. Please could some one explain the process? thank you

What was your logic? You should be trying to find the intercept with the x-axis, so ...

Oh Okay thank you, I'm not sure what my logic was since I didn't know how to approach it This may be a silly question but how do you know when to find the the intercepts with the x axis or the y axis? I think the involvement of the extra variable t is confusing me... I hope this makes sense


(when I saw the MS answer was 1/2pi I thought it was something to do with using the smaller range )

You're trying to use the information given in the diagram to help you. The point O is where x = 0 and y = 0 so doesn't help you find k, because it just corresponds to t = 0. You can see that the curve hits the x-axis again later on, and at this point y = 0 (but x > 0). So you want to start by setting y = tcos(t) = 0. You also know that t can't be 0 because otherwise x would have to be 0 too. So your equation becomes much simpler to solve