Question

If tanx=3, find secx

(Solve for values of x between 0 and 2pi radians)

Answer 1

sec(x) = sqrt(10)

Explanation:

We know that tan(x) = 3.

Using the identity tan^2(x) + 1 = sec^2(x), we can solve for sec(x).

First, let's square both sides of the equation tan(x) = 3:

tan^2(x) = 3^2

tan^2(x) = 9

Next, we can substitute this expression for tan^2(x) into the identity:

tan^2(x) + 1 = sec^2(x)

9 + 1 = sec^2(x)

10 = sec^2(x)

Finally, we can take the square root of both sides to solve for sec(x):

sqrt(10) = sec(x)

Therefore, sec(x) = sqrt(10).