Question

How do you get the exact value of `sec^-1(-2)`?

Answer 1

`(2pi)/3 + 2pin, (4pi)/3 + 2pin`

Explanation:

When working with inverse trig functions, it is better to reverse engineer slightly before you actually evaluate them. In your particular case, this would be rewriting as follows:

`sec(x) = -2`

Keep in mind that you could use any variable for x, I just chose x out of personal preference.

Now, because I've memorised the unit circle, I find it easier to work with sine, cosine and tangent functions. Therefore, I always want to try and get those functions. So, I will rewrite this as:

`1/cos(x) = -2`

Now, if I just go ahead and do some algebra, I get:

`cos(x) = -1/2`

Look familiar? Now we could stop right here and use our unit circle, but since we're talking about inverse trig, I will take it forward just one more step:

`x = cos^-1(-1/2)`

The final answer to this would be `(2pi)/3 + 2pin, (4pi)/3 + 2pin`

If you're unsure how we derived this final answer with the unit circle, or have trouble memorising it, I'd encourage you to watch my video .

Hope that helped :)