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

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3+2sin(pi/2)

3 + 2 sin (\frac{π}{2})

5

Solution steps

3 + 2 sin (\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

= 3 + 2 \cdot 1

Simplify

= 5

sin (arcsin (\frac{12}{13}) + arcsin (\frac{4}{5}))

\frac{9810 sin ( 12 0 ^{\circ} )}{sin ( 9 0 ^{\circ} )}

e^{2 s i n (\frac{7 π}{6})}

tan (\frac{5 π}{9})

sin (2 arccos (\frac{2}{3}))