Trigonometry to Find Angles Flashcards

All 5 cards in this deck

How do you find an angle once you know the value of a trigonometric ratio?

e.g. $\cos x = \frac{15}{18}$

Use the inverse function: $x = \cos^{-1}\left(\frac{15}{18}\right) = 33.6^\circ$ (1 d.p.).

What are the steps to find an angle in a right-angled triangle from two known sides?

e.g. side adjacent to angle $ABC$ is $7$ cm, hypotenuse is $11$ cm

1. Label the known sides for angle $ABC$: $7$ adjacent, $11$ hypotenuse
2. Write the ratio: $\cos ABC = \frac{7}{11}$
3. Use the inverse: $ABC = \cos^{-1}\left(\frac{7}{11}\right) = 50.5^\circ$ (1 d.p.)

What does $\sin^{-1}$ do?

It gives the angle whose sine is that value (the inverse sine function).

True or false? $\sin^{-1} x$ means $\frac{1}{\sin x}$.

False. $\sin^{-1}x$ is the inverse sine — the angle whose sine is $x$.

As an acute angle gets larger, what happens to its cosine?

It decreases, from $\cos 0^\circ = 1$ down to $\cos 90^\circ = 0$.