trig question cot, csc?

Find the exact value of the problem, no decimal form.

{1/[cot(pi/4)]} - {2/[csc(pi/6)]}

please help me, it looks confusing but its, (1 over cotangent of pi/4) minus (2 over cosecant of pi/6)

Thanks

7 Answers

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  • Puggy
    Lv 7
    1 decade ago
    Favorite Answer

    Keep in mind that pi/4 and pi/6 are two familiar values on the unit circle. We know the sine and cosine of them, so all we have to do is convert everything to sine and cosine. cot(x) = cos(x)/sin(x), and csc(x) = 1/sin(x)

    [1/cot(pi/4)] - [2/csc(pi/6)]

    [1/(cos(pi/4)/sin(pi/4)] - [2/(1/sin(pi/6))]

    Now, we have complex fractions, which we can make into simple fractions. I won't show the details, but the above should simplify into

    sin(pi/4)/cos(pi/4) - 2sin(pi/6)

    Now, we solve as normal.

    [sqrt(2)/2] / [sqrt(2)/2] - 2(1/2)

    1 - 1 = 0

  • 1 decade ago

    Well you should know that 1/cot a = tan a & 1/sin a = cosec a

    then the question can be put in the form,

    [1/cot (pi/4)] -2[1/cosec (pi/6)]

    = tan (pi/4) -2.sin (pi/6)

    = 1 -2(1/2)

    = 0

    tan (pi/4) = 1 and sin (pi/6) = 1/2 , can be taken as standard values and verified by constructing right angled triangles.

    hope this helps!

  • 3 years ago

    Csc Pi Over 6

  • 1 decade ago

    what is confusing you?

    your exp= tan pi/4 - 2*sin pi/6

    = 1- 2(.5) = 0

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  • 1 decade ago

    {1/[cot(π/4)]} - {2/[csc(π/6)]}

    = tan(π/4) - 2sin(π/6)

    = 1 - 2(1/2) = 1 - 1 = 0

    A little more familiarity with your trig functions will help you a lot. These are very common angles and the student is expected to know, or be able to quickly calculate, the exact values of trig functions of the angles 0, π/6, π/4, π/3, π/2, π, and multiples thereof.

    Also, if you are unsure of the values of tan, cot, csc, and sec, convert them to sin and cos first. Then calculate.

  • 1 decade ago

    [1/(cos(pi/4)/sin(pi/4))]-[2/(1/sin(pi/6))]=

    [sin(pi/4)/cos(pi/4)]-[(2sin(pi/6)]=

    tan(pi/4)-2sin(pi/6)

    use the trig exact value table remember tan 45(Pi/4)=1 and sin 30(Pi/6)=sqrt(3)/2

    =1-2(sqrt(3)/2)

    =1-sqrt(3) or approximately equals

    = - 0.732050808 to 9 decimal places

  • 1 decade ago

    the answer is 0

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