# pre cal 2

posted by .

Find all solutions in the unterval [0,2pi), cos x/2-sinx=0

• pre cal 2 -

from sin2A = 2sinAcosA we can say that
sinx = 2sin(x/2)cos(x/2)

cos(x/2) = 2sin(x/2)cos(x/2)
1= 2sin(x/2)
sin(x/2) = 1/2
x/2 = 30°, 150° or π/6, 5π/6 radians
x = 60°, 300° or π/3, 5π/3 radians

## Similar Questions

1. ### pre-cal/trig

PlEASE help me with this!! I need it as soon as possible....... cos(x-(pi/4))+sin(x-(pi/4))=1 Find the answer from 0 to 2pi. When I slove this, I got cosx+sinx=(1/ square root of 2). then I don't know what to do the rest. Please help …
2. ### trig

I need to find all solutions of the given equations for the indicated interval. Round solutions to three decimal places if necessary. 1.) 3sin(x)+1=0, x within [0,2pi) 2.) 2sin(sq'd)(x)+cos(x)-1=0, x within R 3.) 4sin(sq'd)(x)-4sin(x)-1=0, …

Determine the solutions for: (cos x)/(1 + sinx) + (1 + sinx)/(cosx) = 2 in the interval x is all real numbers, such that [-2 pi, 2pi]
4. ### Pre-Calculus

cos^2(x) + sin(x) = 1 - Find all solutions in the interval [0, 2pi) I got pi/2 but the answer says {0, pi/2, pi} Where does 0 and pi come from for solutions?
5. ### Pre-Cal

Approximate the equation's soultions in the interval (o, 2pi). If possible find the exact solutions. sin 2x sinx = cosx I do not know where to start.

Approximate the equation's soultions in the interval (o, 2pi). If possible find the exact solutions. sin 2x sinx = cosx I do not know where to start.
7. ### pre cal

Find all solutions in the interval[0,2pi),cos x/2-sinx=0
8. ### Pre-cal

find all solutions of equation in [0, 2pi) 2 (sec x)^2 + (tan x)^2 -3 = 0
9. ### Math Help

Hello! Can someone please check and see if I did this right?
10. ### Math

I need help solving for all solutions for this problem: cos 2x+ sin x= 0 I substituted cos 2x for cos^2x-sin^2x So it became cos^2(x)-sin^2(x) +sinx=0 Then i did 1-sin^2(x)-sin^2(x)+sinx=0 = 1-2sin^2(x)+sinx=0 = sinx(-2sinx+1)=-1 What …

More Similar Questions