SOLUTION: If csc(&#945;) = 3, where 0 < &#945; <&#960; /2, and &#946; is a Quadrant II angle with tan(&#946;) = &#8722;7, find cos &#945; and cos &#946;, sin &#945;and sin &#946; i really

Algebra ->  Trigonometry-basics -> SOLUTION: If csc(&#945;) = 3, where 0 < &#945; <&#960; /2, and &#946; is a Quadrant II angle with tan(&#946;) = &#8722;7, find cos &#945; and cos &#946;, sin &#945;and sin &#946; i really       Log On


   



Question 1113736: If csc(α) = 3, where 0 < α <π /2, and β is a Quadrant II angle with tan(β) = −7, find
cos α and cos β, sin αand sin β
i really need help for this one,please can i have the work so i can understand it ? Thank you

Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
If csc(A) = 3, where 0 < α <π /2, and β is a Quadrant II angle with tan(β) = −7, find
cos α and cos β, sin αand sin β
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Too hard to read.
Don't use squiggles.
Use A instead of alpha.
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Why should I spend time deciphering this?

Answer by ikleyn(52847) About Me  (Show Source):
You can put this solution on YOUR website!
.
1.  If csc(a) = 3 and the angle "a" is in QI, it implies that


    sin(a) = 1%2F3  and  cos(a) = sqrt%281-sin%5E2%28a%29%29 = sqrt%281+-+%281%2F3%29%5E2%29 = sqrt%281-1%2F9%29 = sqrt%288%2F9%29 = %282%2Asqrt%282%29%29%2F3.



2.  If tan(b) = -7  and the angle "b" is in QII, it implies that


    cos^2(b) = 1%2F%281%2Btan%5E2%28b%29%29 = 1%2F%281%2B%28-7%29%5E2%29 = 1%2F50  and  cos(b) = -sqrt%281%2F50%29 = -sqrt%2850%29%2F50 = -%285%2Asqrt%282%29%29%2F50 = -sqrt%282%29%2F10.

    Notice that cos(b) is negative, since "b" is in QII.


    Next, knowing cos(b), you can calculate


    sin(b) = sqrt%281-cos%5E2%28b%29%29 = sqrt%281-2%2F100%29 = sqrt%2898%2F100%29 = %287%2Asqrt%282%29%29%2F10.


Answer.  sin(a) = 1%2F3.  cos(a) = %282%2Asqrt%282%29%29%2F3.  sin(b) = %287%2Asqrt%282%29%29%2F10.  cos(b) = -sqrt%282%29%2F10.