Answer:
1.068.
Step-by-step explanation:
Use the identity
sec^2 O = 1 + tan^2 O
= 1 + (3/8)^2
= 1 9/64
= 73/64
so sec O = √73/8
= 1 .068.
When dealing with radicals and exponents, one must realize that fractional exponents deals directly with radicals. In that sense, sqrt(x) = x^1/2
Now, how to go about doing this:
In a fractional exponent, the numerator represents the actual exponent of the number. So, for x^2/3, the x is being squared.
For the denominator, that deals with the radical. The index, to be exact. The index describes what KIND of radical (or root) is being taken: square, cube, fourth, fifth, and so on. So, for our example x^2/3, x is squared, and that quantity is under a cube root (or a radical with a 3). Here are some more examples to help you understand a bit more:
x^6/5 = Fifth root of x^6
x^3/1 = x^3
^^^Exponential fractions still follow the same rules of simplifying, so...
x^2/4 = x^1/2 = sqrt(x)
Hope this helps!
Step-by-step explanation:
Recall that
Dividing both sides by cosh²(x) gives
Also, recall the identity
Then