# easy trig

posted by .

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.

## Similar Questions

1. ### Trig

Find the exact value of sin2(theta) if cos(theta) = -sqrt 5/3 and 180 < theta < 270. A)-1/9 B)-4 sqrt 5/9 C)1/9 D)4 sqrt 5/9 B?
2. ### simple trig

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?
3. ### Calculus

I wanted to confirm that I solved these problems correctly (we had to convert the polar curves to Cartesian equations). 1.rcos(theta)=1 x=1 2.r=2*sin(theta)+2*cos(theta) r^2=2rsin(theta)+2rcos(theta) x^2+y^2=2y+2x (a little unsure …
4. ### trig

If sin 2 theta = (2/5) in Quadrant 2, find sin theta, cos theta, tan theta, and draw triangle theta.
5. ### Math

1. Let (-7, 4) be a point on the terminal side of (theta). Find the exact values of sin(theta), csc(theta), and cot(theta). 2. Let (theta) be an angle in quadrant IV such that sin(theta)=-2/5. Find the exact values of sec(theta) and …
6. ### Trig

1. Establish the identity: sin(theta+3pi/2)=-cos(theta) 2. Find the exact value of 2(theta) if sin(theta)=5/13 3. Show that: csc2(theta)-cot2(theta)=tan(theta) 4. Find the exact value of tan(cos^-1(square root of 3/2) 5. Approximate …
7. ### Precalculus check answers help!

1.) Find an expression equivalent to sec theta sin theta cot theta csc theta. tan theta csc theta sec theta ~ sin theta 2.) Find an expression equivalent to cos theta/sin theta . tan theta cot theta ~ sec theta csc theta 3.) Simplify …
8. ### Precalculus check answers help!

1.) Find an expression equivalent to sec theta sin theta cot theta csc theta. tan theta csc theta sec theta ~ sin theta 2.) Find an expression equivalent to cos theta/sin theta . tan theta cot theta ~ sec theta csc theta 3.) Simplify …
9. ### trig

If sin theta is equal to 5/13 and theta is an angle in quadrant II find the value of cos theta, sec theta, tan theta, csc theta, cot theta.
10. ### Math Trig Help

sin theta = x/3, with theta in the first quadrant, find the expression for cos theta and tan theta. Answers will be in algebraic terms of x. Give exact answers with 0 < theta <pi/2 (0 less than or equal to theta, less than or …

More Similar Questions