Question

find the exact value of tan(arccos(-2/3))

Answer 1

First, you can replace tan with sin/cos:

\(\tan(\arccos(-\frac{2}{3}))=\dfrac{\sin(\arccos(-\frac{2}{3})) }{\cos(\arccos(-\frac{2}{3}))}\)

The denominator of this expression is -2/3.

Now we "only" have to calculate \(\sin(\arccos(-\frac{2}{3}))\).
Any ideas? (Hint: draw a unit circle and find -2/3 on the x-axis...)

Answer 2

Or you could see that arccos(-2/3) implies that cos y=-2/3
which means that cos^-1 (-2/3) can be substituted for your arccos.
Now, all you have to do is solve tan(2.3005) to get your answer!

Answer 3

@Ianiraegreen: Yeah, but "solving" tan(2.3005) means using your calculator. If you go down that road, you might as well type in the original expression in the calculator.
The "solution" then is just an approximation, not an exact value.
So you really have to try harder I'm afraid :(

Here is the unit circle:

Answer 4

@shaye25: do you have enough information now to solve the last part?

Answer 5

yes thank you

Answer 6

YW!