# Maths

Integration of sine square theta from 0 to 2pi

1. 👍
2. 👎
3. 👁
1. sin^2θ = (1-cos2θ)/2
so, you want
∫[0,2π] 1/2 (1-cos2θ) dθ = 1/2 (θ - 1/2 sin2θ) [0,2π] = π

1. 👍
2. 👎
2. INT sin^2 T dT over t=0 to 2PI
use the half angle formulas sin^2(T)= (1-cos(2T))/2

Int .5*(T-cos(2T)dt
= .5T - .25sin2T over limits
= .5(2PI)-.25sin(4PI)-.5*0+.25(sin(0)=PI

1. 👍
2. 👎
👤
bobpursley

## Similar Questions

1. ### physics

A ball is attached to a string with length of L. It swings in a horizontal circle, with a constant speed. The string makes an angle (theta) with the vertical, and T is the magnitude of the tension in the string. 1)Determine the

2. ### 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.)

3. ### Pre-Calculus

Use a calculator to approximate two values of theta (0

4. ### 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.

1. ### Math:)

Which trigonometric functions are equivalent to tan(theta)? Select all that apply. (2 answers) a. -tan(-theta)**** b. -tan(theta) c. tan(-theta) d. tan(theta+2pi)**** e. tan(theta+pi/2)

2. ### Math

The point (-8,3) lies on the terminal arm of angle theta in standard position. Determine the primary trigonometric ratios for angle theta and calculate the value of theta to the nearest degree. Only the sine ratio was positive,

3. ### Algebra 2

Find the values of the inverse function in radians. sin^-1(0.65) a. 0.71+2pi n and -0.71+2pi n b. 0.71+2pi n and -3.85+2pi n c. 0.86+2pi n and -0.86 +2pi n d. -0.61+2pi n and 2.54+2pi n 2. tan^-1(0.09) a.-0.09+2pi n b. no such

4. ### Math

for what values of theta (0 < theta < 2pi) do maximum r values occur on the graph the polar equation r = 4-3 sin 3 theta

1. ### Calculus

f(theta)= 4sec(theta)+ 2tan(theta), 0 less than theta less than 2pi. find all critical numbers

2. ### Algebra 2

Which cosine function has maximum of 4, a minimum of -4, and a period of 2pi/3? A. y=4 cos 3 theta B. y= 4 cos 2 theta/3 C. y=4 cos theta/3 D. y=4 cos 3 theta

3. ### Algebra 2

What values for theta(0