What is the value of 2cos(-120) ?

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2cos(-120)

2 cos (- 12 0^{\circ})

- 1

Solution steps

2 cos (- 12 0^{\circ})

Rewrite using trig identities:

cos (- 12 0^{\circ}) = - \frac{1}{2}

cos (- 12 0^{\circ})

Use the following property:

cos (- x) = cos (x)

cos (- 12 0^{\circ}) = cos (12 0^{\circ})

= cos (12 0^{\circ})

Use the following trivial identity:

cos (12 0^{\circ}) = - \frac{1}{2}

cos (12 0^{\circ})

cos (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} 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}

= - \frac{1}{2}

= 2 (- \frac{1}{2})

Simplify

2 (- \frac{1}{2}) : - 1

2 (- \frac{1}{2})

Remove parentheses:

(- a) = - a

= - 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

= - 1

sin (36. 5^{\circ})

cos (\frac{π}{3}) - sin (\frac{3 π}{4})

arctan (\frac{16}{8})

sin (7 0^{\circ}) 10

sin (\frac{3 π}{4}) cos (\frac{π}{12}) + cos (\frac{3 π}{4}) sin (\frac{π}{12})