What is the general solution for 5cos(θ)=-5sin(-θ) ?

The general solution for 5cos(θ)=-5sin(-θ) is θ= pi/4+pin

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Popular >

5cos(θ)=-5sin(-θ)

Solution

5 cos (θ) = - 5 sin (- θ)

Solution

θ = \frac{π}{4} + πn

Degrees

θ = 4 5^{\circ} + 18 0^{\circ} n

Solution steps

5 cos (θ) = - 5 sin (- θ)

Rewrite using trig identities

5 cos (θ) = - 5 sin (- θ)

5 cos (θ) = - 5 (- sin (θ))

Simplify

- 5 (- sin (θ)) : 5 sin (θ)

- 5 (- sin (θ))

Apply rule

- (- a) = a

= 5 sin (θ)

5 cos (θ) = 5 sin (θ)

5 cos (θ) = 5 sin (θ)

Subtract

5 sin (θ)

from both sides

5 cos (θ) - 5 sin (θ) = 0

Rewrite using trig identities

5 cos (θ) - 5 sin (θ) = 0

Divide both sides by

cos (θ), cos (θ) \neq = 0

\frac{5 cos ( θ ) - 5 sin ( θ )}{cos ( θ )} = \frac{0}{cos ( θ )}

Simplify

5 - \frac{5 sin ( θ )}{cos ( θ )} = 0

Use the basic trigonometric identity:

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

5 - 5 tan (θ) = 0

5 - 5 tan (θ) = 0

Move

5

to the right side

5 - 5 tan (θ) = 0

Subtract

5

from both sides

5 - 5 tan (θ) - 5 = 0 - 5

Simplify

- 5 tan (θ) = - 5

- 5 tan (θ) = - 5

Divide both sides by

- 5

- 5 tan (θ) = - 5

Divide both sides by

- 5

\frac{- 5 tan ( θ )}{- 5} = \frac{- 5}{- 5}

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

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

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

sec^2(x)+6tan(x)=8

sec^{2} (x) + 6 tan (x) = 8

tan(θ)=-3/8

tan (θ) = - \frac{3}{8}

solvefor i,arcsin(sin(x))=x-2pi solve for

i, arcsin (sin (x)) = x - 2 π

3cos(2θ)+13cos(θ)+5=6cos(θ)

3 cos (2 θ) + 13 cos (θ) + 5 = 6 cos (θ)

Frequently Asked Questions (FAQ)

What is the general solution for 5cos(θ)=-5sin(-θ) ?
The general solution for 5cos(θ)=-5sin(-θ) is θ= pi/4+pin