Mathematics, 11.10.2020 08:01 surfskate
Given the right triangle shown below, prove cos2(θ) + sin2(θ) = 1.
A triangle with sides x, y, and hypotenuse r. Angle theta is opposite to side y.
By
, cos(θ) = StartFraction x Over r EndFraction, and by
, sin(θ) = StartFraction y Over r EndFraction.
Multiplying both sides of the above equations by r, we get that x = r cos(θ) and y = r sin(θ).
The
states that x2 + y2 = r2.
By
, we have [r cos(θ)]2 + [r sin(θ)]2 = r2.
Applying the
, the equation can be written as r2 cos2(θ) + r2 sin2(θ) = r2.
Dividing both sides of the equation by r2 results in cos2(θ) + sin2(θ) = 1.
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Given the right triangle shown below, prove cos2(θ) + sin2(θ) = 1.
A triangle with sides x, y, and...
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