What is the value of 11.5-10.5cos(810) ?

The value of 11.5-10.5cos(810) is 23/2

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11.5-10.5cos(810)

11.5 - 10.5 cos (81 0^{\circ})

\frac{23}{2}

Decimal Notation

11.5

Solution steps

11.5 - 10.5 cos (81 0^{\circ})

= \frac{23}{2} - \frac{21}{2} cos (81 0^{\circ})

Rewrite using trig identities:

cos (81 0^{\circ}) = 0

cos (81 0^{\circ})

cos (81 0^{\circ}) = cos (9 0^{\circ})

cos (81 0^{\circ})

Rewrite

81 0^{\circ}

36 0^{\circ} \cdot 2 + 9 0^{\circ}

= cos (36 0^{\circ} 2 + 9 0^{\circ})

Apply the periodicity of

cos

cos (x + 36 0^{\circ} \cdot k) = cos (x)

cos (36 0^{\circ} \cdot 2 + 9 0^{\circ}) = cos (9 0^{\circ})

= cos (9 0^{\circ})

= cos (9 0^{\circ})

Use the following trivial identity:

cos (9 0^{\circ}) = 0

cos (9 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}

= 0

= 0

= \frac{23}{2} - \frac{21}{2} \cdot 0

Simplify

= \frac{23}{2}

sec (0.43)

\frac{sin ( 9 0 ^{\circ} )}{90}

sin (259. 5^{\circ})

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

\frac{1500}{sin ( 3 0 ^{\circ} )}