What is the general solution for 7cos^2(θ)-9=-9sin(θ) ?

The general solution for 7cos^2(θ)-9=-9sin(θ) is θ=0.28975…+2pin,θ=pi-0.28975…+2pin,θ= pi/2+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

7cos^2(θ)-9=-9sin(θ)

7 cos^{2} (θ) - 9 = - 9 sin (θ)

θ = 0.28975 \dots + 2 πn, θ = π - 0.28975 \dots + 2 πn, θ = \frac{π}{2} + 2 πn

Solution steps

7 cos^{2} (θ) - 9 = - 9 sin (θ)

Subtract

- 9 sin (θ)

from both sides

7 cos^{2} (θ) - 9 + 9 sin (θ) = 0

Rewrite using trig identities

- 2 - 7 sin^{2} (θ) + 9 sin (θ) = 0

Solve by substitution

sin (θ) = \frac{2}{7}, sin (θ) = 1

sin (θ) = \frac{2}{7} : θ = arcsin (\frac{2}{7}) + 2 πn, θ = π - arcsin (\frac{2}{7}) + 2 πn

sin (θ) = 1 : θ = \frac{π}{2} + 2 πn

Combine all the solutions

θ = arcsin (\frac{2}{7}) + 2 πn, θ = π - arcsin (\frac{2}{7}) + 2 πn, θ = \frac{π}{2} + 2 πn

Show solutions in decimal form

θ = 0.28975 \dots + 2 πn, θ = π - 0.28975 \dots + 2 πn, θ = \frac{π}{2} + 2 πn

y, arcsin (y) = x

- 4 cos (2 θ) - 3 cos (θ) - 4 = - 2 cos (θ) - 7

sin (x) + sin (2 x) = sin (3 x)

2 cos^{2} (x) - 9 cos (x) + 4 = 0

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

What is the general solution for 7cos^2(θ)-9=-9sin(θ) ?
The general solution for 7cos^2(θ)-9=-9sin(θ) is θ=0.28975…+2pin,θ=pi-0.28975…+2pin,θ= pi/2+2pin