What is the general solution for 146=(8-cos(θ))^2+(-9-sin(θ))^2 ?

The general solution for 146=(8-cos(θ))^2+(-9-sin(θ))^2 is θ=0.72664…+pin

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146=(8-cos(θ))^2+(-9-sin(θ))^2

146 = (8 - cos (θ))^{2} + (- 9 - sin (θ))^{2}

θ = 0.72664 \dots + πn

Solution steps

146 = (8 - cos (θ))^{2} + (- 9 - sin (θ))^{2}

Switch sides

(8 - cos (θ))^{2} + (- 9 - sin (θ))^{2} = 146

Subtract

146

from both sides

cos^{2} (θ) + sin^{2} (θ) + 18 sin (θ) - 16 cos (θ) - 1 = 0

Rewrite using trig identities

- 16 + 18 tan (θ) = 0

Move

16

to the right side

18 tan (θ) = 16

Divide both sides by

18

tan (θ) = \frac{8}{9}

Apply trig inverse properties

θ = arctan (\frac{8}{9}) + πn

Show solutions in decimal form

θ = 0.72664 \dots + πn

cos (x) = \frac{9}{10}

34 \cdot sin (\frac{π}{6} (x - 4.3)) = 34

2 (sin (x)) 2 - 5 cos (x) - 4 = 0

cos (\frac{x}{2} + 2 0^{\circ}) = sin (x)

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

What is the general solution for 146=(8-cos(θ))^2+(-9-sin(θ))^2 ?
The general solution for 146=(8-cos(θ))^2+(-9-sin(θ))^2 is θ=0.72664…+pin