# Maths

posted by .

Find all the values of x between 0 and 2(pi) for which
sin x + (root 3)cos x = 0

• Maths -

Whenever you see sines and cosines and sqrt 3, draw a thirty, sixty ninety triangle.
the sin of the 60 degree angle is (sqrt 3)/2
the cosine of the 60 degree angle is 1/2
sqrt(3)/2 = (sqrt 3)(1/2)
Now the quadrants where the sine and cosine have opposite signs are quadrant 2 and quadrant four. So look in those two quadrants.

• Maths -

another not necessarily better approach would be ...

sinx = -√3cosx
tanx = -√3

from the same triangle as Damon's we would get a "basic" angle of 60º or pi/3 radians

but the tan is negative in II or IV, so
x = pi - pi/3 or 2pi - pi/3
or x = 2pi/3 or 5pi/3

## Similar Questions

1. ### tigonometry

expres the following as sums and differences of sines or cosines cos8t * sin2t sin(a+b) = sin(a)cos(b) + cos(a)sin(b) replacing by by -b and using that cos(-b)= cos(b) sin(-b)= -sin(b) gives: sin(a-b) = sin(a)cos(b) - cos(a)sin(b) …
2. ### math

Prove that for all real values of a, b, t (theta): (a * cos t + b * sin t)^2 <= a^2 + b^2 I will be happy to critique your work. Start on the left, square it, (a * cos t + b * sin t)^2 = a^2 (1 - sin^2t) + 2ab sin t cost+ b^2 (1 …
3. ### maths

Choose the two options which are true for all values of x 1) cos (x) = cos ( x – pie/2) 2) sin (x + pie/2) = cos (x – pie/2) 3) cos (x) = sin (x – pie/2) 4) sin (x) = sin (x + 4pie) 5) sin (x) = cos (x – pie/2) 6) sin^2 (x) …
4. ### TRIG!

Posted by hayden on Monday, February 23, 2009 at 4:05pm. sin^6 x + cos^6 x=1 - (3/4)sin^2 2x work on one side only! Responses Trig please help! - Reiny, Monday, February 23, 2009 at 4:27pm LS looks like the sum of cubes sin^6 x + cos^6 …
5. ### MATH

1.)Find the exact solution algebriacally, if possible: (PLEASE SHOW ALL STEPS) sin 2x - sin x = 0 2.) GIVEN: sin u = 3/5, 0 < u < ï/2 Find the exact values of: sin 2u, cos 2u and tan 2u using the double-angle formulas. 3.)Use …
6. ### 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))?
7. ### math

use exact values of the sin,cos and tan of (pi/3) and (pi/6)(which I have found)and the symmetry of the graphs of sin,cos and tan to find the exact values of sin(-pi/6), cos(5pi/3) and tan (4pi/3). I know that sin -(pi/6) = -1/2 and …
8. ### math

Use the exact values of the sin, cos and tan of pi/3 and pi/6, and the symmetry of the graphs of sin, cos and tan, to find the exact values of sin -pi/6, cos 5/3pi and tan 4pi/3. I have found the answers to the first three using the …
9. ### Maths

1) Simplification (trigonometric ratios of allied angles)?
10. ### Trigonometry - find all x

Find all x such that 0 <= x <= pi/2 and sin^7 x + cos^7 x = 1. (Be sure to show that no other values of x satisfy the equation.) Well, I know sin^2 x + cos^2 x = 1, and that kind of looks like sin^7 x + cos^7 x = 1. I'm unsure …

More Similar Questions