If cosine is equal to -12/13 Find sine and tangent in Quadrant

• Ephratah7
In summary, The conversation discusses finding the values of sine and tangent in Quadrant two, given the value of cosine. The conversation also includes a diagram and clarification on the use of "^" as the power symbol.
Ephratah7
If cosine is equal to -12/13... Find sine and tangent in Quadrant

If cosine is equal to -12/13... Find sine and tangent in Quadrant Two... What is the answer??

Draw a diagram.

sine = y/r
tangent = y/x
x^2 + y^2 = r^2

Quadrant two means sine>0, and tangent<0.

That should be enough info to solve the problem.

qspeechc said:
Draw a diagram.

sine = y/r
tangent = y/x
x^2 + y^2 = r^2

Quadrant two means sine>0, and tangent<0.

That should be enough info to solve the problem.

... ok, thanks. but what is ^??

Ephratah7 said:
... ok, thanks. but what is ^??

^^... is it "raised to the power of"?

On this and many math boards, if you are just using regular letters, "^" means to the power: 2^3= 8.

Of course, here, you can also use html codes: 2[ sup ]3[ / sup ]= 8, without the spaces, gives 23= 8. Or you can use LaTex: [ tex ]2^3= 8[ /tex ], again without the spaces, gives $$2^3= 8$$. You can see the code used for any LaTex by clicking on it. Also, there is a tutorial for LaTex in the "Homework and Coursework" section.

HallsofIvy said:
On this and many math boards, if you are just using regular letters, "^" means to the power: 2^3= 8.

Of course, here, you can also use html codes: 2[ sup ]3[ / sup ]= 8, without the spaces, gives 23= 8. Or you can use LaTex: [ tex ]2^3= 8[ /tex ], again without the spaces, gives $$2^3= 8$$. You can see the code used for any LaTex by clicking on it. Also, there is a tutorial for LaTex in the "Homework and Coursework" section.

...
i see.. thanks for the info.

"Euclid alone has looked on beauty bare"

^^

1. What is the value of sine if cosine is equal to -12/13?

The value of sine can be found by using the Pythagorean identity: sin^2(x) + cos^2(x) = 1. Therefore, sin(x) = sqrt(1 - cos^2(x)). Plugging in the value of -12/13 for cos(x), we get sin(x) = sqrt(1 - (-12/13)^2) = sqrt(1 - 144/169) = sqrt(25/169) = 5/13.

2. What is the value of tangent if cosine is equal to -12/13?

The value of tangent can be found by dividing sine by cosine: tan(x) = sin(x)/cos(x). Plugging in the values we found for sin(x) and cos(x), we get tan(x) = (5/13)/(-12/13) = -5/12.

3. What quadrant would this point be located in?

A point with a cosine value of -12/13 would be located in the third quadrant, as cosine is negative in the second and third quadrants.

4. Can cosine ever be equal to -12/13 in any other quadrant?

No, cosine can only have a value of -12/13 in the second or third quadrant. In the first quadrant, cosine is always positive, and in the fourth quadrant, it is always negative.

5. How can this information be applied in real-life situations?

Knowing the values of sine, cosine, and tangent in a particular quadrant can be useful in many real-life situations, such as calculating the trajectory of a projectile, determining the optimal angle for solar panels, or designing roller coasters. It is also important in fields such as navigation, engineering, and physics.

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