What is the general solution for -3-5/2*cos(θ)=-3-3cos(θ) ?

The general solution for -3-5/2*cos(θ)=-3-3cos(θ) is θ= pi/2+2pin,θ=(3pi)/2+2pin

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Popular >

-3-5/2*cos(θ)=-3-3cos(θ)

Solution

- 3 - \frac{5}{2} \cdot cos (θ) = - 3 - 3 cos (θ)

Solution

θ = \frac{π}{2} + 2 πn, θ = \frac{3 π}{2} + 2 πn

Degrees

θ = 9 0^{\circ} + 36 0^{\circ} n, θ = 27 0^{\circ} + 36 0^{\circ} n

Solution steps

- 3 - \frac{5}{2} cos (θ) = - 3 - 3 cos (θ)

Solve by substitution

- 3 - \frac{5}{2} cos (θ) = - 3 - 3 cos (θ)

Let:

cos (θ) = u

- 3 - \frac{5}{2} u = - 3 - 3 u

- 3 - \frac{5}{2} u = - 3 - 3 u : u = 0

- 3 - \frac{5}{2} u = - 3 - 3 u

Add

3

to both sides

- 3 - \frac{5}{2} u + 3 = - 3 - 3 u + 3

Simplify

- \frac{5}{2} u = - 3 u

Multiply both sides by

2

- \frac{5}{2} u = - 3 u

Multiply both sides by

2

- \frac{5}{2} u \cdot 2 = - 3 u \cdot 2

Simplify

- \frac{5}{2} u \cdot 2 = - 3 u \cdot 2

Simplify

- \frac{5}{2} u \cdot 2 : - 5 u

- \frac{5}{2} u \cdot 2

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= - \frac{5 \cdot 2}{2} u

Cancel the common factor:

2

= - u \cdot 5

Simplify

- 3 u \cdot 2 : - 6 u

- 3 u \cdot 2

Multiply the numbers:

3 \cdot 2 = 6

= - 6 u

- 5 u = - 6 u

- 5 u = - 6 u

- 5 u = - 6 u

Move

6 u

to the left side

- 5 u = - 6 u

Add

6 u

to both sides

- 5 u + 6 u = - 6 u + 6 u

Simplify

u = 0

u = 0

Substitute back

u = cos (θ)

cos (θ) = 0

cos (θ) = 0

cos (θ) = 0 : θ = \frac{π}{2} + 2 πn, θ = \frac{3 π}{2} + 2 πn

cos (θ) = 0

General solutions for

cos (θ) = 0

cos (x)

periodicity table with

2 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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

θ = \frac{π}{2} + 2 πn, θ = \frac{3 π}{2} + 2 πn

θ = \frac{π}{2} + 2 πn, θ = \frac{3 π}{2} + 2 πn

Combine all the solutions

θ = \frac{π}{2} + 2 πn, θ = \frac{3 π}{2} + 2 πn

Popular Examples

tan(θ)=-6/5

tan (θ) = - \frac{6}{5}

3sec(2θ)=-sqrt(18)

3 sec (2 θ) = - 18

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

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

sin(2θ)= 1/3

sin (2 θ) = \frac{1}{3}

cos^2(θ)=1-sin(θ)

cos^{2} (θ) = 1 - sin (θ)

Frequently Asked Questions (FAQ)

What is the general solution for -3-5/2*cos(θ)=-3-3cos(θ) ?
The general solution for -3-5/2*cos(θ)=-3-3cos(θ) is θ= pi/2+2pin,θ=(3pi)/2+2pin