What is the general solution for 8sin(θ)+15cos(θ)=18 ?

The general solution for 8sin(θ)+15cos(θ)=18 is No Solution for θ\in\mathbb{R}

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8sin(θ)+15cos(θ)=18

8 sin (θ) + 15 cos (θ) = 18

No Solution for θ \in R

Solution steps

8 sin (θ) + 15 cos (θ) = 18

Subtract

15 cos (θ)

from both sides

8 sin (θ) = 18 - 15 cos (θ)

Square both sides

(8 sin (θ))^{2} = (18 - 15 cos (θ))^{2}

Subtract

(18 - 15 cos (θ))^{2}

from both sides

64 sin^{2} (θ) - 324 + 540 cos (θ) - 225 cos^{2} (θ) = 0

Rewrite using trig identities

- 260 - 289 cos^{2} (θ) + 540 cos (θ) = 0

Solve by substitution

cos (θ) = \frac{270}{289} - i \frac{8 35}{289}, cos (θ) = \frac{270}{289} + i \frac{8 35}{289}

cos (θ) = \frac{270}{289} - i \frac{8 35}{289} :

No Solution

cos (θ) = \frac{270}{289} + i \frac{8 35}{289} :

No Solution

Combine all the solutions

No Solution

Verify solutions by plugging them into the original equation

No Solution for θ \in R

\frac{30}{sin ( A )} = \frac{34.4}{sin ( 6 2 ^{\circ} )}

- 2 sin (x) = 1

- 5 sin (x) = - 2 cos^{2} (x) + 4, 0 \leq x \leq 2 π

6 = sin (\frac{π}{4} x) + 5

2 cos (θ) + 1 = 0, 0 \leq θ \leq 2 π

What is the general solution for 8sin(θ)+15cos(θ)=18 ?
The general solution for 8sin(θ)+15cos(θ)=18 is No Solution for θ\in\mathbb{R}