Question

Find an angle `theta` (i) Which increases twice as fast as its cosine. (ii) Whose rate of increase twice is twice the rate of decrease of its consine.

Answer 1

(i) Here, `(d theta)/dt = 2 d/dt(costheta)`
`=> (d theta)/dt = -2sintheta (d theta)/dt`
`=>sin theta = -1/2`
`=> theta = (7pi)/6`.

(ii) Here, `(d theta)/dt = -2 d/dt(costheta)`
`=> (d theta)/dt = 2sintheta (d theta)/dt`
`=>sin theta = 1/2`
`=> theta = pi/6`.