What is the general solution for 8sin(θ)+15cos(θ)=17 ?

The general solution for 8sin(θ)+15cos(θ)=17 is θ=0.48995…+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

8sin(θ)+15cos(θ)=17

8 sin (θ) + 15 cos (θ) = 17

θ = 0.48995 \dots + 2 πn

Solution steps

8 sin (θ) + 15 cos (θ) = 17

Subtract

15 cos (θ)

from both sides

8 sin (θ) = 17 - 15 cos (θ)

Square both sides

(8 sin (θ))^{2} = (17 - 15 cos (θ))^{2}

Subtract

(17 - 15 cos (θ))^{2}

from both sides

64 sin^{2} (θ) - 289 + 510 cos (θ) - 225 cos^{2} (θ) = 0

Rewrite using trig identities

- 225 - 289 cos^{2} (θ) + 510 cos (θ) = 0

Solve by substitution

cos (θ) = \frac{15}{17}

cos (θ) = \frac{15}{17} : θ = arccos (\frac{15}{17}) + 2 πn, θ = 2 π - arccos (\frac{15}{17}) + 2 πn

Combine all the solutions

θ = arccos (\frac{15}{17}) + 2 πn, θ = 2 π - arccos (\frac{15}{17}) + 2 πn

Verify solutions by plugging them into the original equation

θ = arccos (\frac{15}{17}) + 2 πn

Show solutions in decimal form

θ = 0.48995 \dots + 2 πn

8 sin (θ) + 15 cos (θ) = 14

cos (x - 1) = 0

2 sin (t) + 3 cos (t) = 0

tan (θ) = \frac{- \frac{11}{3} - ( - \frac{4}{3} )}{1 + ( - \frac{4}{3} ) ( - \frac{11}{3} )}

csc (2 x) = 2, x 0^{\circ} < x < 36 0^{\circ}

What is the general solution for 8sin(θ)+15cos(θ)=17 ?
The general solution for 8sin(θ)+15cos(θ)=17 is θ=0.48995…+2pin