easy trig

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If sin(theta)=[sqrt(70)]/7 and theta is in Quadrant two, find the exact numerical value of tan theta without using a calculator.

I got tan(theta)=[sqrt(294)]/42

Is that right?

if sin(theta)=-a where 0<a<1, and theta is in quadrant 3, find the exact algebraic expressionm for cos(theta)

  • revised problem, ignore the original post -

    If sin(theta)=[sqrt(7)]/7 and theta is in Quadrant two, find the exact numerical value of tan theta without using a calculator.

    I got tan(theta)=[sqrt(294)]/42

    Is that right?

    if sin(theta)=-a where 0<a<1, and theta is in quadrant 3, find the exact algebraic expressionm for cos(theta)

  • easy trig -

    You posted the same question earlier today, and I told you .....

    http://www.jiskha.com/display.cgi?id=1231449736

  • easy trig -

    yes, but i changed my mistake from
    sin(theta)=[sqrt(70)]/7 to sin(theta)=[sqrt(7)]/7.

    so it's sin(theta)=.378

  • easy trig -

    ok then, that's better

    recall that sine(angle) = opposite/hypotenus

    so we need a right-angled triangle in the II quadrant with a height of √7 and a hypotenuse of 7
    let the base be x
    x^2 + (√7)^2 = 7^2
    x^2 = 42
    x = ±√42, but we are in the second quadrant so x = -√42

    then for yours
    tan(theta) = √7/-√42
    = -1/√6

    notice all steps were done without a calculator.

    that does not mean we couldn't use a calculator to check our answer

    enter the following
    √7/7 =
    2nd function sin
    -180=
    ± key (to make our answer positive in the second quadrant)(on some calculators you might have to multiply by -1 to get it to a positive, do whatever your calc needs done)

    tan =
    store or write down that number

    now do
    -1/√6 =

    compare the two results, they are the same.

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