What is the value of 40sin(72) ?

The value of 40sin(72) is 5sqrt(2)(1+sqrt(5))sqrt(5-\sqrt{5)}

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40sin(72)

40 sin (7 2^{\circ})

52 (1 + 5) 5 - 5

Solution steps

40 sin (7 2^{\circ})

Rewrite using trig identities:

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

= 40 \cdot 2 sin (3 6^{\circ}) cos (3 6^{\circ})

Simplify

= 80 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}

= 80 \cdot \frac{2 5 - 5}{4} \cdot \frac{5 + 1}{4}

Simplify

80 \cdot \frac{2 5 - 5}{4} \cdot \frac{5 + 1}{4} : 52 (1 + 5) 5 - 5

= 52 (1 + 5) 5 - 5

sin (4 5^{\circ}) - sin (4 5^{\circ})

tan (\frac{29 π}{6})

4.5 sin (1 7^{\circ})

5 sin (5 5^{\circ})

\frac{80}{cos ( 6 0 ^{\circ} )}

What is the value of 40sin(72) ?
The value of 40sin(72) is 5sqrt(2)(1+sqrt(5))sqrt(5-\sqrt{5)}