Math

1. On the interval [0, 2pi] what are the solutions to the equation sin3xcos2x =
-cos3xsin2x + 1?
pi/10 and pi/2?

2. What is the value of tan75degrees?
√(3) + 1)/(1 - √(3))?

3. Value of cos(130degrees)cos(130degrees) + sin(10degrees)sin(10degrees)?
Not sure

4. On the interval [0, 2pi] what are the solutions to sin2xcos3x = cos2xsin3x - 1/2
pi/6 and 5pi/6?

5. Value of sin(4pi/9)cos(5pi/18) - cos(4pi/9)sin(5pi/18)?
I'm not sure about my answers, is it root 3/2?

asked by mysterychicken
  1. #1. Since
    sin3xcos2x + cos3xsin2x = sin5x you have
    sin5x = 1
    So, 5x = π/2, 5π/2, ...
    and x = π/10, 5π/10, 9π/10, 13π/10, 17π/10

    You have to keep adding 2π/5 until x gets to 2π

    #2. correct

    #3. Since cos(a-b) = cosa cosb - sina sinb you have
    cos120° = -cos60° = -1/2

    #4. Work like #1
    sin5x = 1/2

    #5. sin (4/9 - 5/18)pi = sin(pi/6) = 1/2
    #4.

    posted by Steve

Respond to this Question

First Name

Your Response

Similar Questions

  1. 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,
  2. Math Help

    Hi! Can someone help check this for me and see if I'm doing it right? Thanks!! :) Directions: Use the Half-Angle formulas to determine the exact value of sin(pi/12). Here's what I have: π/12 = ( 180° ) / 12 = 15°. = sin (
  3. triggggg help

    Let cos 67.5° = [√(2(+√2)]/2, find tan 67.5°. Show work and simplify. I'm not too sure if i'm doing this correct. I know that the given is cos 67.5° = [√(2(+√2)]/2 sin^2 x + cos^2 x = 1 x=67.5° sin^2
  4. Trigonometry

    Solve the equation for solutions in the interval 0<=theta<2pi Problem 1. 3cot^2-4csc=1 My attempt: 3(cos^2/sin^2)-4/sin=1 3(cos^2/sin^2) - 4sin/sin^2 = 1 3cos^2 -4sin =sin^2 3cos^2-(1-cos^2) =4sin 4cos^2 -1 =4sin Cos^2 -
  5. MATH

    Differential equations, initial value problem. The general equation of motion is: mx"+Bx'+kx=f(t), where the independent variable is t, and the displacement x is the dependent variable. In this case, external force f(t)=0, so
  6. 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 +
  7. Please help me with Trig

    Given cos 67.5° = [√(2+√2)]/2, find tan 67.5° , simplify where needed, and show work. I'm starting to learn this stuff, and I'm so confused where to start. I know they gave me the coordinate X as in cos 67.5° =
  8. Math

    The graph of f(x), a trigonometric function, and the graph of g(x) = c intersect at n points over the interval 0 <= x <= 2pi. There are m algebraic solutions to the equation f(x) = g(x), where m > n. Which of the
  9. Trigonometry

    I have some trigonometric equations to do, but I'm pretty lost, and I have to get them done in a timely fashion, so any help would be much appreciated. "Solve the following trig equations. Give all the positive values of the angle
  10. 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)

More Similar Questions