# math (trig)

Find sin(x/2) if sin(x)= -0.4 and 3pi/2 < or equal to (x) < or equal to 2pi

Let's use cos 2A = 1 - 2sin2 A

and we can match
cos x = 1 - 2sin2 (x/2)

so we will need cos x

we know sin x = -.4 and x is in the fourth quadrant, so the cosine will be positive.

Drawing a right angled triangle with side 2 and hypotenuse 5 ( .4 = 4/10 = 2/5), and using Pythagoras it is easy to see that cos x = √21/5

then:
√21/5 = 1 - 2sin2 (x/2)
.
.
.
.
I got sin (x/2) = √(5-√21)/√10 or appr.2043

1. 👍 0
2. 👎 0
3. 👁 206

## Similar Questions

1. ### Calculus

Consider the function f(x)=sin(1/x) Find a sequence of x-values that approach 0 such that (1) sin (1/x)=0 {Hint: Use the fact that sin(pi) = sin(2pi)=sin(3pi)=...=sin(npi)=0} (2) sin (1/x)=1 {Hint: Use the fact that sin(npi)/2)=1

asked by George on September 9, 2008
2. ### Calculus

Consider the function f(x)=sin(1/x) Find a sequence of x-values that approach 0 such that (1) sin (1/x)=0 {Hint: Use the fact that sin(pi) = sin(2pi)=sin(3pi)=...=sin(npi)=0} (2) sin (1/x)=1 {Hint: Use the fact that sin(npi)/2)=1

asked by George on September 9, 2008
3. ### i lied. very quick calc problem.

f(x) = abs(sin(x)), -pi less than or equal to x less than or equal to pi g(x) = x^2 let H(x) = g(f(x)) i got that H(x) would equal sin^2(x). THIS IS WHERE I AM STUCK! find the domain of H. do i still need to account for "-pi less

asked by jane on February 20, 2009
4. ### Math

Test for symmetry with repsect to Q=pi/2, the polar axis, and the pole. r=16cos 3Q r=16cos(3pi/3 + 3h) = 16(cos3pi/2 3h- sin 3pi/2 sin h) cos 3pi/2 = 0 sin 3pi/2 = -1 Not symmetrical My teacher said that this was wrong!Why?

5. ### Math

Test for symmetry with repsect to Q=pi/2, the polar axis, and the pole. r=16cos 3Q r=16cos(3pi/3 + 3h) = 16(cos3pi/2 3h- sin 3pi/2 sin h) cos 3pi/2 = 0 sin 3pi/2 = -1 Not symmetrical My teacher said that this was wrong!Why?

asked by Abbey on May 5, 2010
1. ### Math:)

Explain why sin^-1[sin(3pi/4)] does not = 3pi/4 when y=sin(x) and y=sin^-1(x) are inverses. Any help on this question is greatly appreciated. Thank you!

asked by girly girl on March 20, 2018
2. ### Integral Calculus

Volume of the area bounded by y=sin(x), x-axis, x is greater than or equal to 0 but less than or equal to pi, revolved about x=3pi/2.

asked by Alexa on November 30, 2016
3. ### Trigonometry

Thank you STEVE!!!!! Suppose that Cos (theta) = 1/square root 2 if 0

asked by George on January 23, 2013
4. ### math

Determine all the possible values of x where 0 deg is more than or equal to x and x is more or equal to 360 deg such that i'm not sure the solution, please correct it, sin x sec x - 3 sin x = 0 the solution: sin x 1/cos x - 3 sin

asked by choi2463 on April 15, 2013
5. ### Calculus

I need to find the exact solutions on the interval [0,2pi) for: 2sin^2(x/2) - 3sin(x/2) + 1 = 0 I would start: (2sin(x/2)-1)(sin(x/2)-1) = 0 sin(x/2)=1/2 and sin(x/2)=1 what's next? Ok, what angle has a sin equal to say 1/2 sin

asked by Jen on August 21, 2006

More Similar Questions