The sum of the three smallest positive values of theta such that 4(cos*theta)(sin*theta) = 1 is k*pi. Find k.

Question

Help!!!!!

Answer 1

cos T * sin T = 1/4
so
2 cos T * sin T = 1/2
so
sin 2 T = 1/2
thus
2 T = 30 deg or pi/6 radians
T = pi/12 radians or 15 deg

now cos * sin must be +
so T in quadrant 1 or quadrant 3
so actually T = pi/12 or T = 13pi/12 which is 195 deg

pi/12 + 13 pi/12 + (2pi+pi/12)
= (1/12 +13/12 +24/12 + 1/12)pi
= (39/12)pi
check my arithmetic !

Answer 2

It is saying that 39/12 which is 13/4, is wrong.

Answer 3

2t = π/6 or 5π/6 or 13π/6
t = π/12 or 5π/12 or 13π/12
sum = 19π/12

Answer 4

Thanks steve!!!! It is correct! Also thanks Damon for giving this an attempt!

Answer 5

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