Double Angle Identities (Grade 12 NSC Matric Mathematics): Quizzes

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Double Angle Identities
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What do double angle identities help us find?

Trig values of 2α2α using values of αα

What is the formula for sin⁡2α\sin 2α?

2sin⁡αcos⁡α2 \sin α \cos α

What is the first standard form of cos⁡2α\cos 2α?

cos⁡2α−sin⁡2α\cos^2 α - \sin^2 α

Which is an alternative form of cos⁡2α\cos 2α using sin⁡2α\sin^2 α?

1−2sin⁡2α1 - 2 \sin^2 α

How are double angle identities derived?

From compound angle formulae with α=βα = β

If sin⁡α=0.5\sin α = 0.5 and cos⁡α=0.866\cos α = 0.866, what is sin⁡2α\sin 2α?

0.8660.866

How many equivalent forms does cos⁡2α\cos 2α have?

Three

Which form of cos⁡2α\cos 2α should you use if given only sin⁡α\sin α?

1−2sin⁡2α1 - 2 \sin^2 α

When is tan⁡θ\tan θ undefined?

θ=90°+k×180°θ = 90° + k × 180°, k∈Zk ∈ ℤ

If sin⁡α=35\sin α = \frac{3}{5}, what theorem helps find cos⁡α\cos α?

Pythagoras theorem

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