What is the value of cos(pi)-1 ?

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cos(pi)-1

cos (π) - 1

- 2

Solution steps

cos (π) - 1

Use the following trivial identity:

cos (π) = (- 1)

cos (π)

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)

= - 1 - 1

Simplify

= - 2

(1 2^{2} + 7^{2} - 2 \cdot 12 \cdot 7 \cdot cos (4 0^{\circ}))

cos (2 arccos (\frac{3}{4}) - arccos (\frac{1}{8}))

arcsin (\frac{sin ( 2 5 ^{\circ} )}{1.51})

tan (3 0^{\circ}) + tan (6 0^{\circ})

cos (arctan (\frac{40}{9}) + arccos (\frac{7}{25}))