What is the value of 55-3cos((180(30-30))/(180)) ?

The value of 55-3cos((180(30-30))/(180)) is 52

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55-3cos((180(30-30))/(180))

55 - 3 cos (\frac{180 ( 30 - 30 )}{180})

52

Solution steps

55 - 3 cos (\frac{180 ( 30 - 30 )}{180})

Simplify

= 55 - 3 cos (0)

Use the following trivial identity:

cos (0) = 1

cos (0)

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}

= 1

= 55 - 3 \cdot 1

Simplify

= 52

\frac{4}{cos ( 6 3 ^{\circ} )}

sin (- 34 5^{\circ}) + cos (- 65 0^{\circ})

3 arctan (0)

8 (cos (\frac{3 π}{2}) + i sin (\frac{3 π}{2}))

arcsin (\frac{12}{26})

What is the value of 55-3cos((180(30-30))/(180)) ?
The value of 55-3cos((180(30-30))/(180)) is 52