What is the general solution for 4cos(θ)=-4sin(-θ) ?

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

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Popular >

4cos(θ)=-4sin(-θ)

Solution

4 cos (θ) = - 4 sin (- θ)

Solution

θ = \frac{π}{4} + πn

Degrees

θ = 4 5^{\circ} + 18 0^{\circ} n

Solution steps

4 cos (θ) = - 4 sin (- θ)

Rewrite using trig identities

4 cos (θ) = - 4 sin (- θ)

4 cos (θ) = - 4 (- sin (θ))

Simplify

- 4 (- sin (θ)) : 4 sin (θ)

- 4 (- sin (θ))

Apply rule

- (- a) = a

= 4 sin (θ)

4 cos (θ) = 4 sin (θ)

4 cos (θ) = 4 sin (θ)

Subtract

4 sin (θ)

from both sides

4 cos (θ) - 4 sin (θ) = 0

Rewrite using trig identities

4 cos (θ) - 4 sin (θ) = 0

Divide both sides by

cos (θ), cos (θ) \neq = 0

\frac{4 cos ( θ ) - 4 sin ( θ )}{cos ( θ )} = \frac{0}{cos ( θ )}

Simplify

4 - \frac{4 sin ( θ )}{cos ( θ )} = 0

Use the basic trigonometric identity:

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

4 - 4 tan (θ) = 0

4 - 4 tan (θ) = 0

Move

4

to the right side

4 - 4 tan (θ) = 0

Subtract

4

from both sides

4 - 4 tan (θ) - 4 = 0 - 4

Simplify

- 4 tan (θ) = - 4

- 4 tan (θ) = - 4

Divide both sides by

- 4

- 4 tan (θ) = - 4

Divide both sides by

- 4

\frac{- 4 tan ( θ )}{- 4} = \frac{- 4}{- 4}

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{π}{4} + πn

θ = \frac{π}{4} + πn

Graph

Popular Examples

tan(5x)+tan(3x)=0

tan (5 x) + tan (3 x) = 0

5sin(2x)=5cos(x)

5 sin (2 x) = 5 cos (x)

2cos^2(x)-3cos(x)-5=0

2 cos^{2} (x) - 3 cos (x) - 5 = 0

cos(2x)=-cos(x),0<= x<= 2pi

cos (2 x) = - cos (x), 0 \leq x \leq 2 π

2cos^2(w)+3cos(w)+1=0

2 cos^{2} (w) + 3 cos (w) + 1 = 0

Frequently Asked Questions (FAQ)

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