Trigonometric Identities In Right Angle Triangles

In right angle triangles there is one 90 degree angle and two other angles that are said to be complementary angles on the basis that the sum of interior angles of a triangle is 180 degrees.

Since the two angles A and B are complementary angles they have special properties that allow us to manipulate certain trigonometric identities for right angle triangles. I originally noticed this while I was looking at compound angle formulas and realized that if the angles are complementary then it results in the co-function identities. I then appplied this theory to the Pythagorean identities and proved a new identity for right angle triangles.

The pythagorean identity states that:

sin^2(A)+cos^2(A)=1

sin^2(B)+cos^2(B)=1

In a right angle triangle this translates to:

sin^2(A)+sin^2(B)=1

cos^2(A)+cos^2(B)=1

#Geometry #Trigonometry #TrigonometricIdentities

Easy Math Editor

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Comments

Are you sure that $\sin ^2 A + \cos^2 B = 1$ ? Why?
Shouldn't it be $\sin^2 \theta + \cos^2 \theta = 1$ ?

Calvin Lin Staff - 6 years, 5 months ago

oops yes i will have to edit that, thanks!

Brody Acquilano - 6 years, 5 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$