- #1
CougarXLS
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SOLVED! Thank-you jhicks and Tedjn!
I am taking a basic calculus course and have some weaknesses when it comes to trigonometry. In this case, it's pure trig.
The question states: "Find all values of x in the interval [0,2pi] that satisfy the equation sin x = tan x".
I do know that: tan x = sin x / cos x
Since I know that tan x = sin x / cos x, I can rewrite the above equation sin x = tan x to:
sin x = sin x / cos x
Rearranging and canceling terms, I get:
cos x = 1
So my answer to this problem would be x = 0 and 2pi (in radians, of course), that satisfy the given interval.
I based this answer on the "Trig Functions of Important Angles" and worked out the multiples of pi that satisfied the equation cos x = 1.
My problem is (lol, isn't it always) with the answer key. While they agree that 0 and 2pi are correct, they also add pi. Why? When I consider the cosine of pi (in radians), I get -1, not one. Pi doesn't seem to agree with cos x = 1 when x=pi.
Yet, when I work out sin x = tan x, using x=pi, it works out to 0=0, which is certainly true. How did I miss it? Where'd I go wrong?
I am taking a basic calculus course and have some weaknesses when it comes to trigonometry. In this case, it's pure trig.
Homework Statement
The question states: "Find all values of x in the interval [0,2pi] that satisfy the equation sin x = tan x".
Homework Equations
I do know that: tan x = sin x / cos x
The Attempt at a Solution
Since I know that tan x = sin x / cos x, I can rewrite the above equation sin x = tan x to:
sin x = sin x / cos x
Rearranging and canceling terms, I get:
cos x = 1
So my answer to this problem would be x = 0 and 2pi (in radians, of course), that satisfy the given interval.
I based this answer on the "Trig Functions of Important Angles" and worked out the multiples of pi that satisfied the equation cos x = 1.
My problem is (lol, isn't it always) with the answer key. While they agree that 0 and 2pi are correct, they also add pi. Why? When I consider the cosine of pi (in radians), I get -1, not one. Pi doesn't seem to agree with cos x = 1 when x=pi.
Yet, when I work out sin x = tan x, using x=pi, it works out to 0=0, which is certainly true. How did I miss it? Where'd I go wrong?
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