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

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Further Symmetry Properties and the Pythagorean Identity
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What is another name for complementary relationships in trigonometry?

Cofunction identities

What does sin(π2θ)\sin\left(\frac{\pi}{2} - \theta\right) equal?

cosθ\cos \theta

What does cos(π2θ)\cos\left(\frac{\pi}{2} - \theta\right) equal?

sinθ\sin \theta

What does sin(π2+θ)\sin\left(\frac{\pi}{2} + \theta\right) equal?

cosθ\cos \theta

What does cos(π2+θ)\cos\left(\frac{\pi}{2} + \theta\right) equal?

sinθ-\sin \theta

What is the Pythagorean identity?

cos2θ+sin2θ=1\cos^2\theta + \sin^2\theta = 1

For which values of θ\theta does the Pythagorean identity hold true?

All values

If sinx=35\sin x = \frac{3}{5}, what is cos2x\cos^2 x using the Pythagorean identity?

1625\frac{16}{25}

In which quadrant is cosine negative?

Second quadrant

Which rearrangement of the Pythagorean identity is correct?

sin2θ=1cos2θ\sin^2\theta = 1 - \cos^2\theta

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