Trigonometric identities flashcards

Question 1

What does it mean for two trig expressions to be an identity?

Accepted Answer

An identity is an equation that is true for all values in its domain (where both sides are defined).

Question 2

State the sine sum and difference formulas.

Accepted Answer

$$\sin(\alpha\pm\beta)=\sin\alpha\cos\beta\pm\cos\alpha\sin\beta$$

Question 3

State the half-angle formulas for $\sin\left(\frac{x}{2}\right)$ and $\cos\left(\frac{x}{2}\right)$.

Accepted Answer

$$\sin\left(\frac{x}{2}\right)=\pm\sqrt{\frac{1-\cos x}{2}},\quad \cos\left(\frac{x}{2}\right)=\pm\sqrt{\frac{1+\cos x}{2}}$$
Choose the sign based on the quadrant of $\frac{x}{2}$.

Trigonometric identities flashcards

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