What is the value of 3+2sin(-pi/4) ?

The value of 3+2sin(-pi/4) is 3-sqrt(2)

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3+2sin(-pi/4)

3 + 2 sin (- \frac{π}{4})

3 - 2

Decimal Notation

1.58578 \dots

Solution steps

3 + 2 sin (- \frac{π}{4})

Rewrite using trig identities:

sin (- \frac{π}{4}) = - \frac{2}{2}

sin (- \frac{π}{4})

Use the following property:

sin (- x) = - sin (x)

sin (- \frac{π}{4}) = - sin (\frac{π}{4})

= - sin (\frac{π}{4})

Use the following trivial identity:

sin (\frac{π}{4}) = \frac{2}{2}

sin (\frac{π}{4})

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{2}{2}

= - \frac{2}{2}

= 3 + 2 (- \frac{2}{2})

Simplify

3 + 2 (- \frac{2}{2}) : 3 - 2

3 + 2 (- \frac{2}{2})

Remove parentheses:

(- a) = - a

= 3 - 2 \cdot \frac{2}{2}

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

2 \cdot \frac{2}{2}

Multiply fractions:

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

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

Cancel the common factor:

2

= 2

= 3 - 2

= 3 - 2

sin (2 \cdot 2 5^{\circ})

3 + 2 sin (- \frac{π}{2})

tan (24 0^{\circ}) - tan (21 0^{\circ})

arctan (\frac{3}{1})

9 cos (\frac{π}{4})