What is the value of 1/600*sin(arctan(67/220)) ?

The value of 1/600*sin(arctan(67/220)) is (67sqrt(52889))/(31733400)

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1/600*sin(arctan(67/220))

\frac{1}{600} \cdot sin (arctan (\frac{67}{220}))

\frac{67 52889}{31733400}

Decimal Notation

0.00048 \dots

Solution steps

\frac{1}{600} sin (arctan (\frac{67}{220}))

Rewrite using trig identities:

sin (arctan (\frac{67}{220})) = \frac{( \frac{67}{220} ) 1 + ( \frac{67}{220} ) ^{2}}{1 + ( \frac{67}{220} ) ^{2}}

Use the following identity:

sin (arctan (x)) = \frac{x 1 + x ^{2}}{1 + x ^{2}}

= \frac{( \frac{67}{220} ) 1 + ( \frac{67}{220} ) ^{2}}{1 + ( \frac{67}{220} ) ^{2}}

= \frac{1}{600} \cdot \frac{\frac{67}{220} 1 + ( \frac{67}{220} ) ^{2}}{1 + ( \frac{67}{220} ) ^{2}}

Simplify

= \frac{67 52889}{31733400}

(sin (6 0^{\circ}) + 1)^{2}

59 - 25 cos^{2} (0) - 50 sin (0)

arctan (\frac{2.2907}{1.6326})

sin (- 1 \frac{1}{2})

cos (6 0^{\circ}) 6

What is the value of 1/600*sin(arctan(67/220)) ?
The value of 1/600*sin(arctan(67/220)) is (67sqrt(52889))/(31733400)