# Geometryy

posted by .

given that sec theta = radical13/whole number 3, and csctheta<0 find sin theta using the 2different methods;

1)using the "x-y-r" definition

2) using identities only

• Geometryy -

Timmy, Ryland, Cobra, Jaime -- you must be having an identity crisis tonight.

• Geometryy -

given sec Ø = √13/3 ---> cosØ = 3/√13
also cscØ < 0 ---> sinØ < 0
Ø must be in quadr IV
so x = 3 , r = √13

x^2 + y^2 = r^2
9 + y^2 = 13
y^2 = 4
y = ± 2 , but in IV y = -2

sin Ø = -2/√13

2) you should know that
sin^2Ø + cos^2Ø = 1
sin^2Ø + 9/13 = 1
sin^2Ø = 4/13
sinØ = 2/√13 , but we know that Ø is in IV, where the sine is negative, so
sinØ = -2/√13

## Similar Questions

1. ### Trig Identities

Please help...I'm not understanding trig identities and how to manipulate and express these two problems in their associated functions. Thanks a)Express as a function of cos (theta) 2 sin^2(theta) - 1 b)Express as a function of sin …
2. ### 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 …
3. ### Trigonometry

I don't understand how I'm supposed set the problem up or what theta is... Use the given function value(s), and trigonometric identities (including the cofunction identities), to find the indicated trigonometric functions. sec theta …
4. ### Algebra II

Multiple Choice (theta) means the symbol 0 with the dash in it. 1.)Which expression is equivalent to tan(theta)-(sec(theta))/(sin(theta))?
5. ### Trig

Column 1 Column 2 sec theta - cos theta tan theta sin theta Question: how do you get column 1 to be the same as column 2 ?
6. ### trigonometry

I need help in understanding how to identify which identity to use. using this question as an example. Show that tan theta (sin theta+cot theta cos theata)all over cos theta = sec^2 theta. Please explain.
7. ### Trigonometry

Simplify each expression using fundamental identities. 1. Sin theta cot theta 2. 1-sin^2 theta / cos theta
8. ### Trig

Simplify each expression using fundamental identities. 1. Sin theta cot theta 2. 1-sin^2 theta / cos theta
9. ### Trigonometry

Prove the following identities: 1. (tan theta - sin theta)^2 + (1-cos theta)^2 = (1-sec theta) ^2 2. (1-2cos^2 theta) / sin theta cos theta = tan theta - cot theta 3. (sin theta + cos theta ) ^2 + (sin theta - cos theta ) ^2 = 2 Thank …
10. ### Trigonometry

Prove the following identities: 1. (tan theta - sin theta)^2 + (1-cos theta)^2 = (1-sec theta) ^2 2. (1-2cos^2 theta) / sin theta cos theta = tan theta - cot theta 3. (sin theta + cos theta ) ^2 + (sin theta - cos theta ) ^2 = 2 Thank …

More Similar Questions