What is the value of -sin(pi/2)-cos(pi/2) ?

The value of -sin(pi/2)-cos(pi/2) is -1

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-sin(pi/2)-cos(pi/2)

- sin (\frac{π}{2}) - cos (\frac{π}{2})

- 1

Solution steps

- sin (\frac{π}{2}) - cos (\frac{π}{2})

Use the following trivial identity:

sin (\frac{π}{2}) = 1

sin (\frac{π}{2})

sin (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} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{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} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= 1

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

= - 1 - 0

Simplify

= - 1

\frac{cos ^{2} ( 0 )}{2}

arcsin (\frac{3 \cdot 0.54 \cdot 1 0 ^{- 6}}{\frac{1}{200000}})

\frac{sec ( 3 7 ^{\circ} ) + tan ( 3 7 ^{\circ} )}{sec ( 1 6 ^{\circ} ) + tan ( 1 6 ^{\circ} )}

- sin (- \frac{5 π}{3})

∣ sin (2) ∣

What is the value of -sin(pi/2)-cos(pi/2) ?
The value of -sin(pi/2)-cos(pi/2) is -1