Trig question -sin pi/4 , give the exact value?

In summary, the conversation discusses finding the exact value of -sin pi/4. The answer of -1/root 2 is obtained through the method of finding pi/4 on the unit circle and rationalizing the denominator by multiplying the top and bottom by √2. The conversation also touches on the use of the Pythagorean Theorem and the importance of simplifying radicals in the denominator.
  • #1
Neopets
29
0

Homework Statement



-sin pi/4 , give the exact value?
-1/root 2 is the answer according to the book? How in the world do they get that result. What do you to make that happen?



Homework Equations




The Attempt at a Solution



Also, is this how to do the problem? Find pi/4 on the unit circle, it's root 2 / 2, that doesn't seem to get the right answer even though that's was supposed to be the method?
 
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  • #2
[itex]\frac{1}{\sqrt{2}}[/itex] is the same as [itex]\frac{\sqrt{2}}{2}[/itex], simply "rationalize" it by multiplying the top and bottom by [itex]\sqrt{2}[/itex]

Basically you have the right idea, you can think of sin as the y-coordinate.
Remember, the problem is "negative" sin pi/4.
 
  • #3
  • #4
It is sloppy to leave a radical in the denominator.
 
  • #5
2milehi said:
It is sloppy to leave a radical in the denominator.

Not in all cases :-p
I don't think the teacher would worry so much about it when it comes to trig.
 

Related to Trig question -sin pi/4 , give the exact value?

What is the value of sin(pi/4)?

The value of sin(pi/4) is 1/√2 or approximately 0.707.

How do I find the exact value of sin(pi/4)?

You can use the unit circle or a calculator to find the exact value of sin(pi/4). On the unit circle, the coordinates of the point at pi/4 radians are (√2/2, √2/2). This means that sin(pi/4) = √2/2. With a calculator, you can simply enter sin(pi/4) and get the result as 0.707.

What is the relationship between sin(pi/4) and cos(pi/4)?

Sin(pi/4) and cos(pi/4) are complementary trigonometric functions. This means that sin(pi/4) = cos(pi/2 - pi/4). Using this relationship, we can say that cos(pi/4) = √2/2, which is the exact value of cos(pi/4).

How can I graph sin(pi/4)?

To graph sin(pi/4), you can plot the point (pi/4, √2/2) on a cartesian plane. This point lies on the unit circle and is the exact value of sin(pi/4). You can also use a graphing calculator to get a visual representation of the graph of sin(pi/4).

What are the other trigonometric functions of pi/4?

The other trigonometric functions of pi/4 can be found using the unit circle or a calculator. The values are as follows: cos(pi/4) = √2/2, tan(pi/4) = 1, csc(pi/4) = √2, sec(pi/4) = √2, cot(pi/4) = 1.

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