Math  /  Trigonometry

QuestionQuestion 5 (1 point) Determine the exact value of secπ\sec \pi. 0 -1 1 undefined

Studdy Solution

STEP 1

What is this asking? What's the exact value of secant of pi radians? Watch out! Don't mix up sine, cosine, and secant!
Remember your unit circle values!

STEP 2

1. Define secant
2. Evaluate cosine
3. Calculate secant

STEP 3

Alright, let's **define** what secant even *is*!
Secant is the reciprocal of cosine.
So, sec(x)=1cos(x)\sec(x) = \frac{1}{\cos(x)}.
It's like flipping cosine upside down!

STEP 4

Now, we need to figure out cos(π)\cos(\pi).
Think about the unit circle!
At π\pi radians, we're all the way on the left side, at the point (1,0)(-1, 0).

STEP 5

The x-coordinate of that point gives us the cosine value.
So, cos(π)=1\cos(\pi) = -1.
Boom!

STEP 6

Now we can **put it all together**!
We have sec(π)=1cos(π)\sec(\pi) = \frac{1}{\cos(\pi)}.
We just figured out that cos(π)=1\cos(\pi) = -1, so we can **substitute** that in: sec(π)=11\sec(\pi) = \frac{1}{-1}.

STEP 7

And finally, 11=1\frac{1}{-1} = -1.
So, sec(π)=1\sec(\pi) = -1.
We did it!

STEP 8

The exact value of sec(π)\sec(\pi) is **-1**.

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