What is the value of 100*sin(72) ?

The value of 100*sin(72) is (25sqrt(2)(sqrt(5)+1)sqrt(5-\sqrt{5)})/2

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100*sin(72)

100 \cdot sin (7 2^{\circ})

\frac{25 2 ( 5 + 1 ) 5 - 5}{2}

Solution steps

100 sin (7 2^{\circ})

Rewrite using trig identities:

sin (7 2^{\circ}) = 2 sin (3 6^{\circ}) cos (3 6^{\circ})

= 100 \cdot 2 sin (3 6^{\circ}) cos (3 6^{\circ})

Simplify

= 200 sin (3 6^{\circ}) cos (3 6^{\circ})

Rewrite using trig identities:

sin (3 6^{\circ}) = \frac{2 5 - 5}{4}

Rewrite using trig identities:

cos (3 6^{\circ}) = \frac{5 + 1}{4}

= 200 \cdot \frac{2 5 - 5}{4} \cdot \frac{5 + 1}{4}

Simplify

200 \cdot \frac{2 5 - 5}{4} \cdot \frac{5 + 1}{4} : \frac{25 2 ( 5 + 1 ) 5 - 5}{2}

= \frac{25 2 ( 5 + 1 ) 5 - 5}{2}

45 sin (4 5^{\circ})

cot (6 9^{\circ})

cos (- \frac{9 π}{2})

sin (- \frac{35 π}{6})

2 sec^{2} (\frac{π}{2})

What is the value of 100*sin(72) ?
The value of 100*sin(72) is (25sqrt(2)(sqrt(5)+1)sqrt(5-\sqrt{5)})/2