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

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3-3cos(pi/2)

3 - 3 cos (\frac{π}{2})

3

Solution steps

3 - 3 cos (\frac{π}{2})

Use the following trivial identity:

cos (\frac{π}{2}) = 0

cos (\frac{π}{2})

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}

= 0

= 3 - 3 \cdot 0

Simplify

= 3

arccos (\frac{20}{35})

\frac{( 1 - cos ( 15 0 ^{\circ} ) )}{sin ( 15 0 ^{\circ} )}

80 cot (6 0^{\circ})

75 0^{2} + 90 0^{2} - 2 \cdot 750 \cdot 900 \cdot [cos (9 5^{\circ})]

cos (- 6 0^{\circ}) - tan (- 4 5^{\circ})