What is the general solution for 1+cot^2(θ)=1.33 ?

The general solution for 1+cot^2(θ)=1.33 is θ=1.04937…+pin,θ=2.09222…+pin

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1+cot^2(θ)=1.33

1 + cot^{2} (θ) = 1.33

θ = 1.04937 \dots + πn, θ = 2.09222 \dots + πn

Degrees

θ = 60.12451 \dots^{\circ} + 18 0^{\circ} n, θ = 119.87548 \dots^{\circ} + 18 0^{\circ} n

Solution steps

1 + cot^{2} (θ) = 1.33

Solve by substitution

1 + cot^{2} (θ) = 1.33

Let:

cot (θ) = u

1 + u^{2} = 1.33

1 + u^{2} = 1.33 : u = 0.33, u = - 0.33

1 + u^{2} = 1.33

Move

1

to the right side

1 + u^{2} = 1.33

Subtract

1

from both sides

1 + u^{2} - 1 = 1.33 - 1

Simplify

u^{2} = 0.33

u^{2} = 0.33

For

x^{2} = f (a)

the solutions are

x = f (a), - f (a)

u = 0.33, u = - 0.33

Substitute back

u = cot (θ)

cot (θ) = 0.33, cot (θ) = - 0.33

cot (θ) = 0.33, cot (θ) = - 0.33

cot (θ) = 0.33 : θ = arccot (0.33) + πn

cot (θ) = 0.33

Apply trig inverse properties

cot (θ) = 0.33

General solutions for

cot (θ) = 0.33

cot (x) = a \Rightarrow x = arccot (a) + πn

θ = arccot (0.33) + πn

θ = arccot (0.33) + πn

cot (θ) = - 0.33 : θ = arccot (- 0.33) + πn

cot (θ) = - 0.33

Apply trig inverse properties

cot (θ) = - 0.33

General solutions for

cot (θ) = - 0.33

cot (x) = - a \Rightarrow x = arccot (- a) + πn

θ = arccot (- 0.33) + πn

θ = arccot (- 0.33) + πn

Combine all the solutions

θ = arccot (0.33) + πn, θ = arccot (- 0.33) + πn

Show solutions in decimal form

θ = 1.04937 \dots + πn, θ = 2.09222 \dots + πn

x, r + s - 6 t = cos (2 x + y)

cos (x) + cos^{3} (x) = 0

- 2 cos (\frac{θ}{2}) = 0

cos (x) = - \frac{3}{4}, tan (x) i s

cos (θ) = \frac{- 1}{3}

What is the general solution for 1+cot^2(θ)=1.33 ?
The general solution for 1+cot^2(θ)=1.33 is θ=1.04937…+pin,θ=2.09222…+pin