Posted by jen on .
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 
jen,
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 
Reiny,
You posted the same question earlier today, and I told you .....
http://www.jiskha.com/display.cgi?id=1231449736 
easy trig 
jen,
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 
Reiny,
ok then, that's better
recall that sine(angle) = opposite/hypotenus
so we need a rightangled 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.