What is the general solution for cos(u)-1.5sin^2(u)+0.1667=0 ?

The general solution for cos(u)-1.5sin^2(u)+0.1667=0 is u=0.84108…+2pin,u=2pi-0.84108…+2pin

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cos(u)-1.5sin^2(u)+0.1667=0

cos (u) - 1.5 sin^{2} (u) + 0.1667 = 0

u = 0.84108 \dots + 2 πn, u = 2 π - 0.84108 \dots + 2 πn

Solution steps

cos (u) - 1.5 sin^{2} (u) + 0.1667 = 0

Rewrite using trig identities

- 1.3333 + cos (u) + 1.5 cos^{2} (u) = 0

Solve by substitution

cos (u) = \frac{- 1 + 8.9998}{3}, cos (u) = \frac{- 1 - 8.9998}{3}

cos (u) = \frac{- 1 + 8.9998}{3} : u = arccos (\frac{- 1 + 8.9998}{3}) + 2 πn, u = 2 π - arccos (\frac{- 1 + 8.9998}{3}) + 2 πn

cos (u) = \frac{- 1 - 8.9998}{3} :

No Solution

Combine all the solutions

u = arccos (\frac{- 1 + 8.9998}{3}) + 2 πn, u = 2 π - arccos (\frac{- 1 + 8.9998}{3}) + 2 πn

Show solutions in decimal form

u = 0.84108 \dots + 2 πn, u = 2 π - 0.84108 \dots + 2 πn

3 sin (2 x - 1) = 1

m, sec (m + 1 2^{\circ}) = csc (4 2^{\circ} - n)

1 tan (x) = 3

tan (x) = \frac{1.6}{4}

sin^{2} (x) + 7 sin^{2} (x) + 5 cos^{2} (x) + 3 = 0

What is the general solution for cos(u)-1.5sin^2(u)+0.1667=0 ?
The general solution for cos(u)-1.5sin^2(u)+0.1667=0 is u=0.84108…+2pin,u=2pi-0.84108…+2pin