How would you solve this?

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Answer 1 · 2018-05-02T05:44:06

#t=0,pi,1.4274,6.1403#

Here,

#14sintcost=8sint#

#=>14sintcost-8sint=0#

#=>2sint(7cost-1)=0#

#=>2sint=0 or 7cost-1=0#

#=>sint=0 or cost=1/7,where,t in[0,2pi)#

#(i)sint=0=>t=0,pi.#

#(ii)cost=1/7 > 0=>I^(st) or IV^(th) Quadrant#

#=>t=1.4274 or t=6.1403#

Hence,

#t=0,pi,1.4274,6.1403#

Answer 2 · 2018-05-02T10:21:28

#t = 0, pi, text{Arc}text{cos}(4/7), 2pi-text{Arc}text{cos}(4/7)#

I'll leave the calculator stuff to you.

# 14 sin t cos t - 8 sin t = 0#

#2 sin t (7 cos t - 4) = 0#

#sin t = 0# or #cos t = 4/7#

#t = 0, pi, text{Arc}text{cos}(4/7), 2pi-text{Arc}text{cos}(4/7)#

I don't like how they ruin a nice exact answer with approximations, so I stop here.