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

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

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-3cos(pi/3)-2sin(pi/3)

- 3 cos (\frac{π}{3}) - 2 sin (\frac{π}{3})

- \frac{3}{2} - 3

Decimal Notation

- 3.23205 \dots

Solution steps

- 3 cos (\frac{π}{3}) - 2 sin (\frac{π}{3})

Use the following trivial identity:

cos (\frac{π}{3}) = \frac{1}{2}

cos (\frac{π}{3})

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}

= \frac{1}{2}

Use the following trivial identity:

sin (\frac{π}{3}) = \frac{3}{2}

sin (\frac{π}{3})

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{3}{2}

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

Simplify

- 3 \cdot \frac{1}{2} - 2 \cdot \frac{3}{2} : - \frac{3}{2} - 3

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

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

3 \cdot \frac{1}{2}

Multiply fractions:

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

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

Multiply the numbers:

1 \cdot 3 = 3

= \frac{3}{2}

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

2 \cdot \frac{3}{2}

Multiply fractions:

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

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

Cancel the common factor:

2

= 3

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

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

arcsec (\frac{3}{4})

sin (- 93 0^{\circ})

\frac{2}{3} arctan (2) 3

2 sin (3 0^{\circ}) - 2 sin (4 5^{\circ})

(sin (3 0^{\circ}) - cos (3 0^{\circ})) (sin (3 0^{\circ}) + cos (3 0^{\circ}))

What is the value of -3cos(pi/3)-2sin(pi/3) ?
The value of -3cos(pi/3)-2sin(pi/3) is -3/2-sqrt(3)