What is the general solution for 271.63=(3sqrt(3)*169.7)/pi cos(α) ?

The general solution for 271.63=(3sqrt(3)*169.7)/pi cos(α) is α=0.25464…+2pin,α=2pi-0.25464…+2pin

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271.63=(3sqrt(3)*169.7)/pi cos(α)

271.63 = \frac{3 3 \cdot 169.7}{π} cos (α)

α = 0.25464 \dots + 2 πn, α = 2 π - 0.25464 \dots + 2 πn

Degrees

α = 14.59036 \dots^{\circ} + 36 0^{\circ} n, α = 345.40963 \dots^{\circ} + 36 0^{\circ} n

Solution steps

271.63 = \frac{3 3 \cdot 169.7}{π} cos (α)

Switch sides

\frac{3 3 \cdot 169.7}{π} cos (α) = 271.63

Simplify

\frac{3 3 \cdot 169.7}{π} : \frac{3 \cdot 509.1}{π}

\frac{3 3 \cdot 169.7}{π}

Multiply the numbers:

3 \cdot 169.7 = 509.1

= \frac{3 \cdot 509.1}{π}

\frac{3 \cdot 509.1}{π} cos (α) = 271.63

Multiply both sides by

π

\frac{3 \cdot 509.1}{π} cos (α) = 271.63

Multiply both sides by

π

\frac{3 \cdot 509.1}{π} cos (α) π = 271.63 π

Simplify

881.78706 \dots cos (α) = 853.35081 \dots

881.78706 \dots cos (α) = 853.35081 \dots

Divide both sides by

881.78706 \dots

881.78706 \dots cos (α) = 853.35081 \dots

Divide both sides by

881.78706 \dots

\frac{881.78706 \dots cos ( α )}{881.78706 \dots} = \frac{853.35081 \dots}{881.78706 \dots}

Simplify

cos (α) = 0.96775 \dots

cos (α) = 0.96775 \dots

Apply trig inverse properties

cos (α) = 0.96775 \dots

General solutions for

cos (α) = 0.96775 \dots

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = 2 π - arccos (a) + 2 πn

α = arccos (0.96775 \dots) + 2 πn, α = 2 π - arccos (0.96775 \dots) + 2 πn

α = arccos (0.96775 \dots) + 2 πn, α = 2 π - arccos (0.96775 \dots) + 2 πn

Show solutions in decimal form

α = 0.25464 \dots + 2 πn, α = 2 π - 0.25464 \dots + 2 πn

2 sin (t) cos (t) + sin (t) - 2 cos (t) - 1 = 0

4 cos^{2} (\frac{x}{2}) - 3 = 0

sin (2 θ) + cos (θ) = 0, 0 \leq θ \leq 2 π

sin (1 0^{\circ}) = 2 sin (a) cos (a)

cos^{2} (x) = 2 + 2 sin (x), 0 \leq x \leq 2 π

What is the general solution for 271.63=(3sqrt(3)*169.7)/pi cos(α) ?
The general solution for 271.63=(3sqrt(3)*169.7)/pi cos(α) is α=0.25464…+2pin,α=2pi-0.25464…+2pin