Question 721005: Find the value of s in the interval (0, pi/2) that makes the statement true. Round to four decimal places. sec s= 5.4169. I don't understand how to get started on this and I am sure it is very simple! I will have several questions like this on my midterm and know I HAVE to understand how to work them. Thanks in advance.
Answer by DrBeeee(684)   (Show Source):
You can put this solution on YOUR website! What you are given is the trig function, secant. The question is to find the angle, s, whose secant (written as sec) is 5.4169. Here's how this any any similar problem can be solved.
You should be given, or required to know that
(1) sec(s) = 1/cos(s) where we know that cos stands for cosine, a basic function on your scientific calculator.
Now you can set (1) equal to 5.4169 and get
(2) 1/cos(s) = 5.4169 or
inverting (flipping) both sides of (2) we get
(3) cos(s) = 1/5.4169 or
(4) cos(s) = 0.1846...
Now just take the inverse cos of (4) and get
(5) s = cos^(-1)(0.1846...) or
(6) s = 79.36175... degrees
Understand so far? If not here's a one line summary
(7) s = cos^(-1)(1/5.4169)
We're not finished!
You need to calculate s in radians, not degrees, in the range (0,pi/2). You can do this be changing your calculator to operate in radians or use the conversion from degrees to radians as follows
(8) s = (pi/180)*(79.361...) or
(9) s = 1.3851239
Answer: s = 1.3851 rad. to the nearest fourth decimal.
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