Further Symmetry Properties and the Pythagorean Identity (VCE SSCE Mathematical Methods): Flashcards

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Further Symmetry Properties and the Pythagorean Identity
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Another name for complementary relationships

Cofunction identities

Value of sin⁡(π2−θ)\sin\left(\frac{\pi}{2} - \theta\right)

cos⁡θ\cos \theta

Value of cos⁡(π2−θ)\cos\left(\frac{\pi}{2} - \theta\right)

sin⁡θ\sin \theta

Value of sin⁡(π2+θ)\sin\left(\frac{\pi}{2} + \theta\right)

cos⁡θ\cos \theta

Value of cos⁡(π2+θ)\cos\left(\frac{\pi}{2} + \theta\right)

−sin⁡θ-\sin \theta

The Pythagorean identity formula

cos⁡2θ+sin⁡2θ=1\cos^2\theta + \sin^2\theta = 1

Range of θ\theta for which Pythagorean identity holds

All values of θ\theta

Rearrangement: sin⁡2θ=?\sin^2\theta = ? using Pythagorean identity

1−cos⁡2θ1 - \cos^2\theta

Rearrangement: cos⁡2θ=?\cos^2\theta = ? using Pythagorean identity

1−sin⁡2θ1 - \sin^2\theta

What to check when using Pythagorean identity for sign

The quadrant the angle is in

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