Find the value of cos(x), given that sin(x) = -4/5 and π ≤ x ≤ 3π/2

[Raged]

Find the value of cos(x), given that sin(x) = -4/5 and π ≤ x ≤ 3π/2

I need to find cos(x) given sin(x)=-4/5 and [FONT=&quot]π [/FONT][FONT=&quot]≤ x [/FONT][FONT=&quot]≤[/FONT][FONT=&quot] 3[/FONT][FONT=&quot]π/2. I'm not sure what to do with that last tidbit of information but I solved it anyways without using it. (The [/FONT][FONT=&quot]π [/FONT][FONT=&quot]≤ x [/FONT][FONT=&quot]≤[/FONT][FONT=&quot] 3[/FONT][FONT=&quot]π/2).
I got cos(x)= 3/5 but I'm not sure how x being greater than or equal to [/FONT][FONT=&quot]π[/FONT][FONT=&quot] and less than or equal to [/FONT][FONT=&quot]3π/2 would affect it.[/FONT]

 

[stapel]

Sine is positive, for angles in QIII (i.e., between 180° and 270°).

Um... Are you sure about that...?

 

[stapel]

I need to find cos(x) given sin(x)=-4/5 and π ≤ x ≤ 3π/2. I'm not sure what to do with that last tidbit of information but I solved it anyways without using it. (The π ≤ x ≤ 3π/2).
I got cos(x)= 3/5 but I'm not sure how x being greater than or equal to π and less than or equal to 3π/2 would affect it.

First, draw the picture. This angle is in the third quadrant, so it looks like:

place-holder triangle:

                       ^ y
                       |
                       |
                       |
----*------------------*----------->
    |//////////////////|
    |//////////////    |
    |//////////        |
    |//////            |
    |//                |
    *                  |

You know that sine is "opposite over hypotenuse", so you know to label the triangle's opposite side and hypotenuse as:

place-holder triangle:

                       ^ y
                       |
                       |
                       |
----*------------------*----------->
    |//////////////////|
-4  |//////////////    |
    |//////////        |
    |//////     5      |
    |//                |
    *                  |

You can then apply the Pythagorean Theorem to find the value of the adjacent side (being the side on the x-axis).

By putting this triangle in the third quadrant, we have shown ourselves which should be the sign ("plus" or "minus") on that adjacent side's number. (Since sine is negative in two quadrants, but cosine is only negative in one of those two, they had to give us quadrant info, in order for us to answer the question. By the way, this information also tells us that your proposed solution cannot be correct.)

 

[mmm4444bot]

Um... Are you sure about that...?

Doh! :shock: I had read sin and cos, and started thinking tan.