Trig Identities #2 Pythagorean Identities

trig 2

Above is a quick refresher on each trig function. You only really need sin, cos, tan – but for convenience:

tan(\theta ) = \frac{sin(\theta )}{cos(\theta )}

(think SOHCAHTOA on the unit circle)

csc(\theta ) = \frac{1}{sin(\theta )}

sec(\theta ) = \frac{1}{cos(\theta )}

cot(\theta ) = \frac{1}{tan(\theta )} = \frac{cos(\theta )}{sin(\theta )}

tr2

Recall the formula of a circle is

x^2+y^2=1

and if our x and y coordinates (cos(\theta), sin(\theta)) lie on the circle (which they do) then:

cos^2{\theta } + sin^2{\theta } = 1

Take this identity and divide both sides by sin^2{\theta } :

\frac{cos^2(\theta )}{sin^2(\theta)} + 1 = \frac{1}{sin^2(\theta)}

cot^2(\theta)+1=csc^2(\theta)

We could instead have divded both sides by cos^2{\theta}  :

1+ \frac{sin^2(\theta )}{cos^2(\theta)} = \frac{1}{cos^2(\theta)}

1 + tan^2(\theta) = sec^2(\theta)

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One thought on “Trig Identities #2 Pythagorean Identities

  1. Pingback: Trig Identities #3 Periodicity | Solve My Maths

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