solve if you can

Geometry Level 3

arc sin(sin3)+arc sin(sin4)+arc sin(sin5)=?

HINT:where 3,4&5 are in radians

none of these 12 -2 2

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Hemanth Koundinya by Hemanth Koundinya , 23, India

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1 solution

Marta Reece
Jun 10, 2017

arcsin ⁡ ( sin ⁡ 3 ) = π − 3 \arcsin(\sin3)=\pi-3

arcsin ⁡ ( sin ⁡ 4 ) = π − 4 \arcsin(\sin4)=\pi-4

arcsin ⁡ ( sin ⁡ 5 ) = 5 − 2 π \arcsin(\sin5)=5-2\pi

arcsin ⁡ ( sin ⁡ 3 ) + arcsin ⁡ ( sin ⁡ 4 ) + arcsin ⁡ ( sin ⁡ 5 ) = π − 3 + π − 4 + 5 − 2 π = − 2 \arcsin(\sin3)+\arcsin(\sin4)+\arcsin(\sin5)=\pi-3+\pi-4+5-2\pi=\boxed{-2}

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