Right Triangle Trigonometry Flashcards

Question 1

State the definition of $\sin	heta$ in right triangle trigonometry.

Accepted Answer

$$\sin	heta=\frac{	ext{opposite}}{	ext{hypotenuse}}$$ for an acute angle $	heta$ in a right triangle.

Question 2

State the Pythagorean identity for sine and cosine.

Accepted Answer

$$\sin^2	heta+\cos^2	heta=1$$ (true for any angle where sine and cosine are defined).

Question 3

In a $45^\circ\!	ext{-}45^\circ\!	ext{-}90^\circ$ triangle, what are the side ratios (leg : leg : hypotenuse), and what is $	an 45^\circ$?

Accepted Answer

Side ratios: $$1:1:\sqrt{2}$$ and $$	an 45^\circ=\frac{1}{1}=1.$$

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