What is the general solution for 4cos^2(x)+17sin(x)=8 ?

The general solution for 4cos^2(x)+17sin(x)=8 is x=0.25268…+2pin,x=pi-0.25268…+2pin

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4cos^2(x)+17sin(x)=8

4 cos^{2} (x) + 17 sin (x) = 8

x = 0.25268 \dots + 2 πn, x = π - 0.25268 \dots + 2 πn

Solution steps

4 cos^{2} (x) + 17 sin (x) = 8

Subtract

8

from both sides

4 cos^{2} (x) + 17 sin (x) - 8 = 0

Rewrite using trig identities

- 4 + 17 sin (x) - 4 sin^{2} (x) = 0

Solve by substitution

sin (x) = \frac{1}{4}, sin (x) = 4

sin (x) = \frac{1}{4} : x = arcsin (\frac{1}{4}) + 2 πn, x = π - arcsin (\frac{1}{4}) + 2 πn

sin (x) = 4 :

No Solution

Combine all the solutions

x = arcsin (\frac{1}{4}) + 2 πn, x = π - arcsin (\frac{1}{4}) + 2 πn

Show solutions in decimal form

x = 0.25268 \dots + 2 πn, x = π - 0.25268 \dots + 2 πn

cos^{4} (x) = 1 - 8 sin^{2} (x) cos^{2} (x)

tan (x) = \frac{10}{18}

\frac{( 1 + cot ^{2} ( x ) )}{cos ^{2} ( x )} = cot^{2} (x)

sin (2 p + 1) = - 1

y, a \cdot z = 5 sin (2 y)

What is the general solution for 4cos^2(x)+17sin(x)=8 ?
The general solution for 4cos^2(x)+17sin(x)=8 is x=0.25268…+2pin,x=pi-0.25268…+2pin