trigonometry

5. Find the complete exact solution of sin x = -√3/2.

9. Solve cos 2x – 3sin x cos 2x = 0 for the principal value(s) to two decimal places.

21. Solve tan^2x + tan x – 1 = 0 for the principal value(s) to two decimal places.

22. Prove that tan^2a� – 1 + cos^2a = tan^2a sin^2a

  1. 0
  2. 0
  3. 3
asked by eemily
  1. 5. From the 30-60-90° triangle we know
    sin 60° = +√3/2
    so x must be in quadrants III or IV
    x = 180+60= 240° or x = 360-60 = 300°
    or x = 4π/3 or x = 5π/3

    9.
    cos 2x(1 - 3sinx) = 0
    cos 2x = 0 or sinx = 1/3

    for cos 2x = 0
    2x = 90° or 2x = 270°
    x = 45° or x = 135°
    since the period of cos 2x is 180° , two other answers are 225° and 315°
    x = π/4 , 3π/4 , 5π/4 and 7π/4

    for sinx = 1/3
    x = 19.47° or x = 160.53°

    10. Using the quadratic equation we have
    tan x = (-1 ±√5)/2
    if tanx = (-1+√5)/2 , then x = 31.72° or 211.72°
    if tanx = (-1 - √5)/2 , then x = 121.72 or 301.72°

    22.
    LS = tan^2 a - 1 + cos^2 a
    = sec^2 a -1 -1 + cos^2 a
    = 1/cos^2 a - 2 + cos^2 a
    = (1 - 2cos^2 a + cos^4 a)/cos^2 a
    = (cos^2 a - 1)^2 /cos^2 A
    = (-sin^2 a)^2 / cos^2 a
    = sin^4 a / cos^2 a
    = sin^2 a / cos^2 a (sin^2 a)
    = tan^2 a sin^2 a
    = RS

    1. 0
    2. 0
    posted by Reiny

Respond to this Question

First Name

Your Response

Similar Questions

  1. trig help much appreciated! :))

    1. Find the complete exact solution of sin x = . 2. Solve cos 2x – 3sin x cos 2x = 0 for the principal value(s) to two decimal places. 3. Solve tan2 x + tan x – 1 = 0 for the principal value(s) to two decimal places. 4. Prove

    asked by suzy on August 16, 2013
  2. 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 the

    asked by MAKITA on April 11, 2009
  3. trigonometry

    5.Find the complete exact solution of sin x = -√3/2. 10. Solve cos 2x – 3sin x cos 2x = 0 for the principal value(s) to two decimal places. 12. Solve tan^2x + tan x – 1 = 0 for the principal value(s) to two decimal places.

    asked by Jose on December 16, 2012
  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 +

    asked by hayden on February 24, 2009
  5. Trig hep, please? Thank you!

    1. Find the exact value of sin(195(degrees)) 2. If cot2(delta)=5/12 with 0(

    asked by Michelle on August 18, 2013
  6. Trigonometry

    4. Find the exact value for sin(x+y) if sinx=-4/5 and cos y = 15/17. Angles x and y are in the fourth quadrant. 5. Find the exact value for cos 165degrees using the half-angle identity. 1. Solve: 2 cos^2x - 3 cosx + 1 = 0 for 0

    asked by Tiffany Enlow on April 10, 2009
  7. Math

    Evaluate *Note - We have to find the exact value of these. That I know to do. For example sin5π/12 will be broken into sin (π/6) + (π/4) So... sin 5π/12 sin (π/6) + (π/4) sin π/6 cos π/4 + cos π/6 sin π/4 I get all those

    asked by Anonymous on November 25, 2007
  8. Calculus 12th grade (double check my work please)

    1.)Find dy/dx when y= Ln (sinh 2x) my answer >> 2coth 2x. 2.)Find dy/dx when sinh 3y=cos 2x A.-2 sin 2x B.-2 sin 2x / sinh 3y C.-2/3tan (2x/3y) D.-2sin2x / 3 cosh 3yz...>> my answer. 2).Find the derivative of y=cos(x^2) with

    asked by anon on March 6, 2011
  9. 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 si -pi/6, cos 5/3pi and tan 4pi/3. I have found the answers to the first three using

    asked by jenny on August 24, 2011
  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)

    asked by Pablo on November 26, 2006

More Similar Questions