how do you solve Trigonometric equations ?

Question

sec x=1

Answer 1

1/cosx=1
cosx=1
x = 0

Answer 2

Usually, by looking up in tables or by putting the function in an Excel spreadsheet.

If you know the value and are trying to find the angle, the function is called arc-(something).
e.g.,
arc-secant (symbol = arcsec).
You are trying to find x in
arcsec(1) = x

You may have to use some identities in order to transform the function you have into one that is given in tables or that Excel can solve.

For example, sec(x) = 1/cos(x)

There are rarely tables that give secant directly but there are many that give sine and cosine (and tangent often enough).

If sec(x) = 1 then
cos(x) = 1/sec(x) = 1/1 = 1

arccos(1) = 0 (degrees or radians, same thing at zero)

x is 0 or any value equivalent to a full circumference (multiples of 360 degrees or 2*pi radian).

In Excel, the answer is always given in radians. There are pi radians in 180 degrees.

So if you need degrees, multiply the Excel spreadsheet answer by 180/pi (approx. 57.29577951 degrees per radian).

However, Excel does not do arcsec, and some older versions can only do arctan.

Answer 3

If you are more familiar with sin(x), cos(x) and tan(x), convert the equation into terms containing sin(x), cos(x) and tan(x).

sec(x) = 1
1/cos(x) = 1
cos(x) = 1

cos(x) = 1 when x = 2nπ

x = 2nπ where 'n' is an integer