What is the general solution for 3sin^2(x)=8cos(x) ?

The general solution for 3sin^2(x)=8cos(x) is x=1.23095…+2pin,x=2pi-1.23095…+2pin

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3sin^2(x)=8cos(x)

3 sin^{2} (x) = 8 cos (x)

x = 1.23095 \dots + 2 πn, x = 2 π - 1.23095 \dots + 2 πn

Solution steps

3 sin^{2} (x) = 8 cos (x)

Subtract

8 cos (x)

from both sides

3 sin^{2} (x) - 8 cos (x) = 0

Rewrite using trig identities

(1 - cos^{2} (x)) \cdot 3 - 8 cos (x) = 0

Solve by substitution

cos (x) = - 3, cos (x) = \frac{1}{3}

cos (x) = - 3 :

No Solution

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

Combine all the solutions

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

Show solutions in decimal form

x = 1.23095 \dots + 2 πn, x = 2 π - 1.23095 \dots + 2 πn

7 cos (x) - 24 sin (x) = 10

4 cos (2 θ) + 1 = 2 cos (θ)

sin (2 x) = - 2 cos^{2} (x), 0 \leq x \leq 2 π

2 sin^{3} (x) = 2 sin (x)

\frac{2 cos ( θ )}{tan ( θ )} = cot (θ)

What is the general solution for 3sin^2(x)=8cos(x) ?
The general solution for 3sin^2(x)=8cos(x) is x=1.23095…+2pin,x=2pi-1.23095…+2pin