What is the value of cos(90+45) ?

The value of cos(90+45) is -(sqrt(2))/2

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cos(90+45)

cos (9 0^{\circ} + 4 5^{\circ})

- \frac{2}{2}

Decimal Notation

- 0.70710 \dots

Solution steps

cos (9 0^{\circ} + 4 5^{\circ})

Simplify

= cos (13 5^{\circ})

Use the following trivial identity:

cos (13 5^{\circ}) = - \frac{2}{2}

cos (13 5^{\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{2}{2}

= - \frac{2}{2}

csc (- 2)

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

- sin (0.4)

- sin (0.5)

\frac{tan ( 6 0 ^{\circ} ) - tan ( 2 0 ^{\circ} )}{1 + tan ( 6 0 ^{\circ} ) tan ( 2 0 ^{\circ} )}