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Description
Geometry/Trigonometry hell, if you can figure this out, help a girl out and comment the answers. The original questions was.
"Draw a 30-60-90 triangle. Label all angle measures and side relationships. Using the side relationships from the figure, show that the following trigonometric identities hold true for the given angles:
a) tan 60* = sin 60*/cos 60*
b) sin^2 (30*) + cos^2 (30*) = 1"
So call up all the mathemagicians, geometry guinesses, and trigonometry buffs, help a poor girl out.
"Draw a 30-60-90 triangle. Label all angle measures and side relationships. Using the side relationships from the figure, show that the following trigonometric identities hold true for the given angles:
a) tan 60* = sin 60*/cos 60*
b) sin^2 (30*) + cos^2 (30*) = 1"
So call up all the mathemagicians, geometry guinesses, and trigonometry buffs, help a poor girl out.
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Comments3
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A:
Tan(60) = s root 3 / s
Sin(60) = s root 3 / S
Cos(60) = s / S
(s root 3 / s) = (s root 3 * S) / (s * S)
= (s root 3 / S) / (s / S)
B:
Sin(30) = s / S
Cos(30) = s root 3 / S
((s * s) / (S * S)) + ((s root 3 * s root 3) / (S * S))
= ((s * s) + (s root 3 * s root 3)) / (S * S)
= ((s * s) * (1 + (root 3 * root 3))) / (4 * s * s)
= ((s * s) * (1 + 3)) / (4 * s * s)
= (4 * s^2) / (4 * s^2)
= 1
Can you follow all that?
Tan(60) = s root 3 / s
Sin(60) = s root 3 / S
Cos(60) = s / S
(s root 3 / s) = (s root 3 * S) / (s * S)
= (s root 3 / S) / (s / S)
B:
Sin(30) = s / S
Cos(30) = s root 3 / S
((s * s) / (S * S)) + ((s root 3 * s root 3) / (S * S))
= ((s * s) + (s root 3 * s root 3)) / (S * S)
= ((s * s) * (1 + (root 3 * root 3))) / (4 * s * s)
= ((s * s) * (1 + 3)) / (4 * s * s)
= (4 * s^2) / (4 * s^2)
= 1
Can you follow all that?