What is the general solution for 8sin(θ)+15cos(θ)=0 ?

The general solution for 8sin(θ)+15cos(θ)=0 is θ=-1.08083…+pin

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8sin(θ)+15cos(θ)=0

8 sin (θ) + 15 cos (θ) = 0

θ = - 1.08083 \dots + πn

Degrees

θ = - 61.92751 \dots^{\circ} + 18 0^{\circ} n

Solution steps

8 sin (θ) + 15 cos (θ) = 0

Rewrite using trig identities

8 sin (θ) + 15 cos (θ) = 0

Divide both sides by

cos (θ), cos (θ) \neq = 0

\frac{8 sin ( θ ) + 15 cos ( θ )}{cos ( θ )} = \frac{0}{cos ( θ )}

Simplify

\frac{8 sin ( θ )}{cos ( θ )} + 15 = 0

Use the basic trigonometric identity:

\frac{sin ( x )}{cos ( x )} = tan (x)

8 tan (θ) + 15 = 0

8 tan (θ) + 15 = 0

Move

15

to the right side

8 tan (θ) + 15 = 0

Subtract

15

from both sides

8 tan (θ) + 15 - 15 = 0 - 15

Simplify

8 tan (θ) = - 15

8 tan (θ) = - 15

Divide both sides by

8

8 tan (θ) = - 15

Divide both sides by

8

\frac{8 tan ( θ )}{8} = \frac{- 15}{8}

Simplify

tan (θ) = - \frac{15}{8}

tan (θ) = - \frac{15}{8}

Apply trig inverse properties

tan (θ) = - \frac{15}{8}

General solutions for

tan (θ) = - \frac{15}{8}

tan (x) = - a \Rightarrow x = arctan (- a) + πn

θ = arctan (- \frac{15}{8}) + πn

θ = arctan (- \frac{15}{8}) + πn

Show solutions in decimal form

θ = - 1.08083 \dots + πn

What is the general solution for 8sin(θ)+15cos(θ)=0 ?
The general solution for 8sin(θ)+15cos(θ)=0 is θ=-1.08083…+pin