What is the value of 3+2*sin(pi/6) ?

The value of 3+2*sin(pi/6) is 4

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3+2*sin(pi/6)

3 + 2 \cdot sin (\frac{π}{6})

4

Solution steps

3 + 2 sin (\frac{π}{6})

Use the following trivial identity:

sin (\frac{π}{6}) = \frac{1}{2}

sin (\frac{π}{6})

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}

= \frac{1}{2}

= 3 + 2 \cdot \frac{1}{2}

Simplify

3 + 2 \cdot \frac{1}{2} : 4

3 + 2 \cdot \frac{1}{2}

2 \cdot \frac{1}{2} = 1

2 \cdot \frac{1}{2}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot 2}{2}

Cancel the common factor:

2

= 1

= 3 + 1

Add the numbers:

3 + 1 = 4

= 4

= 4

sec (0.2)

\frac{sin ( 12 0 ^{\circ} )}{π}

sin (\frac{- 1 π}{3})

sin (\frac{49 π}{6}) + tan (\frac{41 π}{4})

75 tan (2 5^{\circ})