Is cos((piθ)/2)=-0.25 ?

The answer to whether cos((piθ)/2)=-0.25 is False

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prove cos((piθ)/2)=-0.25

prove

cos (\frac{π θ}{2}) = - 0.25

False

Solution steps

cos (\frac{π θ}{2}) = - 0.25

Show that the two sides are not equal

For

cos (\frac{π θ}{2}) = - 0.25

plug in

θ = 0

cos (\frac{π 0}{2}) = 1

cos (\frac{π 0}{2})

Simplify

= 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

cot (x) + \frac{1}{cot ( x )} = sin (x) cos (x)

\frac{sin ( 2 a )}{1 - sin ^{2} ( a )} = 2 tan (a)

cos (t) = sin (t + \frac{π}{2})

0 = csc^{2} (x) + 2 cot (x)

\frac{sin ^{2} ( t )}{tan ( t )} = sin (t) cos (t)