What is the general solution for 3cos(θ)=3sin(-θ) ?

The general solution for 3cos(θ)=3sin(-θ) is θ=(3pi)/4+pin

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Popular >

3cos(θ)=3sin(-θ)

Solution

3 cos (θ) = 3 sin (- θ)

Solution

θ = \frac{3 π}{4} + πn

Degrees

θ = 13 5^{\circ} + 18 0^{\circ} n

Solution steps

3 cos (θ) = 3 sin (- θ)

Rewrite using trig identities

3 cos (θ) = 3 sin (- θ)

3 cos (θ) = 3 (- sin (θ))

Simplify

3 (- sin (θ)) : - 3 sin (θ)

3 (- sin (θ))

Remove parentheses:

(- a) = - a

= - 3 sin (θ)

3 cos (θ) = - 3 sin (θ)

3 cos (θ) = - 3 sin (θ)

Subtract

- 3 sin (θ)

from both sides

3 cos (θ) + 3 sin (θ) = 0

Rewrite using trig identities

3 cos (θ) + 3 sin (θ) = 0

Divide both sides by

cos (θ), cos (θ) \neq = 0

\frac{3 cos ( θ ) + 3 sin ( θ )}{cos ( θ )} = \frac{0}{cos ( θ )}

Simplify

3 + \frac{3 sin ( θ )}{cos ( θ )} = 0

Use the basic trigonometric identity:

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

3 + 3 tan (θ) = 0

3 + 3 tan (θ) = 0

Move

3

to the right side

3 + 3 tan (θ) = 0

Subtract

3

from both sides

3 + 3 tan (θ) - 3 = 0 - 3

Simplify

3 tan (θ) = - 3

3 tan (θ) = - 3

Divide both sides by

3

3 tan (θ) = - 3

Divide both sides by

3

\frac{3 tan ( θ )}{3} = \frac{- 3}{3}

Simplify

tan (θ) = - 1

tan (θ) = - 1

General solutions for

tan (θ) = - 1

tan (x)

periodicity table with

πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

θ = \frac{3 π}{4} + πn

θ = \frac{3 π}{4} + πn

Graph

Popular Examples

sqrt(3)tan((2x)/3)+1=0

3 tan (\frac{2 x}{3}) + 1 = 0

sin(x)= 11/61

sin (x) = \frac{11}{61}

sin^3(x)=-sin^2(x)

sin^{3} (x) = - sin^{2} (x)

cos(θ)= 4/5 ,sin(θ)

cos (θ) = \frac{4}{5}, sin (θ)

3cos(2θ)-3cos(θ)+3=4cos(θ)+10

3 cos (2 θ) - 3 cos (θ) + 3 = 4 cos (θ) + 10

Frequently Asked Questions (FAQ)

What is the general solution for 3cos(θ)=3sin(-θ) ?
The general solution for 3cos(θ)=3sin(-θ) is θ=(3pi)/4+pin