# trig

Hi, I need to find the domain and rnge of the following:
1. X= 1/2 (cos theta + theta sin theta)
Y=1/2 (sin theta - theta cos theta)

total guess here, but here goes
Domain cos theta = +/- 1 and domain sin theta = +/- 1 so domain theta sin theta = 0- +/-infinity
so domain of X= 1/2 (cos theta + theta sin theta) = 1/2 - +/- infinity
Then range with similar logic of Y=1/2 (sin theta - theta cos theta) = 0 - +/- infinity

Last, domain if x = cot theta

Thank yu

Range using similar logic

asked by Courtney
1. As usual, the domain is the set of values for x where the function is defined.

x = 1/2 (cosθ + θsinθ)
domain is all real numbers.
range is all real numbers, since θsinθ oscillates between θ and -θ.

y = 1/2 (sinθ - θcosθ)
same domain and range as for x

This graph is a pair of spirals, starting at (1,0) and expanding outwards, clockwise for t<0, counterclockwise for t>0

posted by Steve

First Name

Your Answer

## Similar Questions

1. ### 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
2. ### Algebra II

Multiple Choice Which expression is NOT equivalent to 1? (theta) means 0 with dash in it. A.)sin^2 (theta)+cot^2 (theta) sin^2 (theta) B.)(sin^(theta))/(1-cos(theta))-cos(theta) C,)sec^2 (theta)+ tan^2 (theta) D.)(cot^2(theta)
3. ### Trig

Which expression equivalent to: cos(theta + pi/2). A)cos theta B)-cos theta C)sin theta D)-sin theta my book doesnt give examples of this but my crack at it would be C b/c distributive property? and 2cos theta = sin theta
4. ### Physics

An object is shot at 20m/s at an angle theta. The object lands 24m away. What is the angle? Can you check if I am doing this right? I had v(initial) = 20 m/s g = 9.8 m/s^2 x = 24m 1st I solved for time: x = v(initial) t x =
5. ### precalc h

sin(theta)/1-cos(theta) + 1-cos(theta)/sin(theta) = 2csc(theta) That question makes absolutely no sense.. could someone help me? or lead me in the direction to figuring it out? and.. (Beside the trig functions is theta) 1+1/cos =
6. ### 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.
7. ### trigonometry

can you correct the rest for me please? Express each as a function of theta: a. sin (270deg + theta)= cos theta b. cos (pi + theta)= -cos theta c. tan (810 + theta)= ????? d. sin (theta - 180)= -sin theta
8. ### trigonomtry

can you correct the rest for me please? Express each as a function of theta: a. sin (270deg + theta)= cos theta b. cos (pi + theta)= -cos theta c. tan (810 + theta)= ????? d. sin (theta - 180)= -sin theta
9. ### trigonometry

can you correct the rest for me please? Express each as a function of theta: a. sin (270deg + theta)= cos theta b. cos (pi + theta)= -cos theta c. tan (810 + theta)= ????? d. sin (theta - 180)= -sin theta
10. ### trig

Hi there! I NEED SERIOUS HELP, PLEASE!!! i have such a hard time with verifying identities! The question is: [(sin(theta/2)) / csc(theta/2)] + [(cos (theta/2) / sec(theta/2)] = 1 I have a few ideas on how to solve this, but am

More Similar Questions