Is cos(0+pi/2)=-sin(θ) ?

The answer to whether cos(0+pi/2)=-sin(θ) is False

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prove cos(0+pi/2)=-sin(θ)

prove

cos (0 + \frac{π}{2}) = - sin (θ)

False

Solution steps

cos (0 + \frac{π}{2}) = - sin (θ)

Show that the two sides are not equal

For

cos (0 + \frac{π}{2}) = - sin (θ)

plug in

θ = 1

cos (0 + \frac{π}{2}) = 0

cos (0 + \frac{π}{2})

Simplify

= cos (\frac{π}{2})

Use the following trivial identity:

cos (\frac{π}{2}) = 0

cos (\frac{π}{2})

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}

= 0

= 0

- sin (1) = - 0.84147 \dots

- sin (1)

Refine to a decimal form

= - 0.84147 \dots

The two sides are not equal

\Rightarrow False