Is cos(θ)=(sqrt(11))/6 ?

The answer to whether cos(θ)=(sqrt(11))/6 is False

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prove cos(θ)=(sqrt(11))/6

prove

cos (θ) = \frac{11}{6}

False

Solution steps

cos (θ) = \frac{11}{6}

Show that the two sides are not equal

For

cos (θ) = \frac{11}{6}

plug in

θ = 0

cos (0) = 1

cos (0)

Use the following trivial identity:

cos (0) = 1

cos (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}

= 1

= 1

The two sides are not equal

\Rightarrow False

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cos (0) sin (0) = - sin (0)

3 sin (x^{2}) + 4 cos^{2} (x) = 3 + cos^{2} (x)