What is the value of 2+3cos(pi/2) ?

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2+3cos(pi/2)

2 + 3 cos (\frac{π}{2})

2

Solution steps

2 + 3 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

= 2 + 3 \cdot 0

Simplify

= 2

\frac{1}{cos ( \frac{3 π}{2} )}

cot (1 0^{\circ}) - cot (8 0^{\circ})

sin^{2} (\frac{π}{6}) + cos^{2} (\frac{π}{3})

sec (arcsin (- 2))

- cot (\frac{3 π}{4}) \cdot csc (\frac{3 π}{4})