What is the general solution for 20sin^2(x)+27cos(x)=6 ?

The general solution for 20sin^2(x)+27cos(x)=6 is x=1.98231…+2pin,x=-1.98231…+2pin

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20sin^2(x)+27cos(x)=6

20 sin^{2} (x) + 27 cos (x) = 6

x = 1.98231 \dots + 2 πn, x = - 1.98231 \dots + 2 πn

Solution steps

20 sin^{2} (x) + 27 cos (x) = 6

Subtract

6

from both sides

20 sin^{2} (x) + 27 cos (x) - 6 = 0

Rewrite using trig identities

14 - 20 cos^{2} (x) + 27 cos (x) = 0

Solve by substitution

cos (x) = - \frac{2}{5}, cos (x) = \frac{7}{4}

cos (x) = - \frac{2}{5} : x = arccos (- \frac{2}{5}) + 2 πn, x = - arccos (- \frac{2}{5}) + 2 πn

cos (x) = \frac{7}{4} :

No Solution

Combine all the solutions

x = arccos (- \frac{2}{5}) + 2 πn, x = - arccos (- \frac{2}{5}) + 2 πn

Show solutions in decimal form

x = 1.98231 \dots + 2 πn, x = - 1.98231 \dots + 2 πn

cos^{2} (x) = cos^{2} (x) - sin^{2} (x)

arctan (x) = \frac{2.73}{7.5}

y, sin (x) + cos (y) = ln (x)

- 8 csc^{2} (x) - 4 cot (x) = - 12

2 cos (2 x) + 43 sin (x) = 5

What is the general solution for 20sin^2(x)+27cos(x)=6 ?
The general solution for 20sin^2(x)+27cos(x)=6 is x=1.98231…+2pin,x=-1.98231…+2pin