{"id":2312,"date":"2022-09-30T09:26:00","date_gmt":"2022-09-30T03:56:00","guid":{"rendered":"http:\/\/physicscatalyst.com\/article\/?p=2312"},"modified":"2022-11-04T12:06:27","modified_gmt":"2022-11-04T06:36:27","slug":"trigonometry-formulas-for-class-11","status":"publish","type":"post","link":"https:\/\/physicscatalyst.com\/article\/trigonometry-formulas-for-class-11\/","title":{"rendered":"Trigonometry Formulas for class 11 (PDF download)"},"content":{"rendered":"\n
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Trigonometry Formulas for class 11<\/span> <\/strong><\/span><\/h2>\n\n\n\n

(PDF download)<\/strong><\/span><\/p>\n\n\n\n

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Trigonometry is quite an interesting subject. Here are the useful Trigonometry Formulas for class 11 Maths<\/a><\/p>\n\n\n\n

Basic Formula<\/strong><\/p>\n\n\n\n

$tan(x) =  \\frac {sin(x)}{cos(x)}$<\/p>\n\n\n\n

$cot(x) = \\frac {cos(x)}{sin(x)}$<\/p>\n\n\n\n

Reciprocal Identities:<\/strong><\/p>\n\n\n\n

$cosec(x) = \\frac {1}{sin(x)}$<\/p>\n\n\n\n

$sec(x) =\\frac { 1}{cos(x)}$<\/p>\n\n\n\n

$cot(x) = \\frac {1}{tan(x)}$<\/p>\n\n\n\n

$sin(x) = \\frac {1}{cosec(x)}$<\/p>\n\n\n\n

$cos(x) = \\frac {1}{sec(x)}$<\/p>\n\n\n\n

$tan(x) = \\frac {1}{cot(x)}$<\/p>\n\n\n\n

Pythagorean Identities:<\/strong><\/p>\n\n\n\n

$sin^2(x) + cos^2(x) = 1$<\/p>\n\n\n\n

$cot^2x +1 = cosec^2x$<\/p>\n\n\n\n

$1+tan^2x = sec^2x$<\/p>\n\n\n\n

Trigonometric Ratio\u2019s of Common angles<\/strong><\/p>\n\n\n\n

We can find the values of trigonometric ratio\u2019s various angle<\/p>\n\n\n\n

\"Trigonometry<\/figure>\n\n\n\n

Trigonometry Formula for Complementary and supplementary angles<\/strong><\/p>\n\n\n\n

\"Trigonometry<\/a><\/figure>\n\n\n\n

Sin and cos function<\/u><\/p>\n\n\n\n

  1. $cos(A+B)=cos(A)cos(B)-sin(A)sin(B)$<\/li>
  2. $cos(A-B)=cos(A)cos(B)+sin(A)sin(B)$<\/li>
  3. $cos(\\pi \/2 -A)=sin(A)$<\/li>
  4. $sin(\\pi \/2 -A)=cos(A)$<\/li>
  5. $sin(A+B)=sin(A)cos(B)+sin(B)cos(A)$<\/li>
  6. $sin(A-B)=sin(A)cos(B)-sin(B)cos(A)$<\/li><\/ol>\n\n\n\n

    Tan and cot functions<\/u><\/p>\n\n\n\n

    If none of the angles x, y and (x + y) is an odd multiple of $\\pi \/2$<\/p>\n\n\n\n

    $tan(A+B)=\\frac{tan(A)+tan(B)}{1-tan(A)tan(B)}$<\/p>\n\n\n\n

    $tan(A-B)=\\frac{tan(A)-tan(B)}{1+tan(A)tan(B)}$<\/p>\n\n\n\n

    If none of the angles x, y and (x + y) is a multiple of $\\pi \/2$<\/p>\n\n\n\n

    $cot(A+B)=\\frac{cot(A)cot(B)-1}{cot(A)+cot(B)}$<\/p>\n\n\n\n

    $cot(A-B)=\\frac{cot(A)cot(B)+1}{cot(B)-cot(A)}$<\/p>\n\n\n\n

    Some more Trigonometric Functions<\/strong>
    Double of x (Double Of Angles)<\/u><\/p>\n\n\n\n

    $cos2x=cos^{^{2}}x-sin^{^{2}}x=2cos^{^{2}}x-1=1-2sin^{^{2}}x=\\frac{1-tan^{^{2}}x}{1+tan^{^{2}}x}$
    $sin2x=2cos(x)sin(x)=\\frac{2tan(x)}{1+tan^{^{2}}x}$
    $tan2x=\\frac{2tan(x)}{1-tan^{^{2}}x}$<\/p>\n\n\n\n

    Triple of x ( Triple of Angles)<\/u><\/p>\n\n\n\n

    $sin3x=3sin(x)-4sin^{3}x$
    $cos3x=4cos^{3}x-3cos(x)$<\/p>\n\n\n\n

    $tan(3x)=\\frac{3tanx-tan^{^{3}}x}{1-3tan^{^{2}}x}$<\/p>\n\n\n\n

    Sum and Difference of Angles<\/strong><\/p>\n\n\n\n

    $cos(A)+cos(B)=2cos\\frac{A+B}{2}cos\\frac{A-B}{2}$
    $cos(A)-cos(B)=-2sin\\frac{A+B}{2}sin\\frac{A-B}{2}$
    $sin(A)+sin(B)=2sin\\frac{A+B}{2}cos\\frac{A-B}{2}$
    $sin(A)-sin(B)=2cos\\frac{A+B}{2}sin\\frac{A-B}{2}$<\/p>\n\n\n\n

    Half Angle Formula<\/strong><\/p>\n\n\n\n

    \"Trigonometry<\/a><\/figure>\n\n\n\n

    Pythagoras’ Identities in Radical form<\/strong><\/p>\n\n\n\n

    \"\"<\/a><\/figure>\n\n\n\n

    Power Reducing Functions<\/strong><\/p>\n\n\n\n

    \"Trigonometry<\/a><\/figure>\n\n\n\n

    Trigonometric equations Formula’s<\/strong><\/p>\n\n\n\n

    1.$sin x = 0$ implies  $x = n \\pi$, where n is any integer<br>
    2.$cos x = 0$ implies $x = (2n + 1)(\\pi \/2)$<br><\/p>\n\n\n\n

    1. $sinx =siny$ then $x=n \\pi + (-1)^{n}y$ where n is any integer<br><\/li>
    2. $cosx=cosy$ then $x=2n \\pi + y$ or $x=2n \\pi – y$ where n is any integer<br><\/li>
    3. $tanx=tany$ then $x=n \\pi +y$ where n is any integer<br><\/li><\/ol>\n\n\n\n

      5. Equation of the form
      $sin^2x = sin^2 y, cos^2 x = cos^2 y , tan^2 x = tan^2 y$
      The general solution is given by
      $x = n \\pi \\pm y$ where n is any integer<\/p>\n\n\n\n

      6. Equation of the Form
      |sin x|=1 ,General solution is given by $x= (2n+1) \\frac {\\pi}{2}$<br>
      |cos x|=1, general solution is given by $x=n \\pi$<br><\/p>\n\n\n\n

      Some basics Tips to solve the trigonometry questions<\/strong><\/p>\n\n\n\n

      (1) Always try to bring the multiple angles to single angles using the basic formula. Make sure all your angles are the same. Using $sin(2x)$ and $sin(x)$ is difficult, but if you use $sin(2x) = 2 sin(x)cos(x)$, that leaves $sin(x)$ and $cos(x)$, and now all your functions match. The same goes for addition and subtraction: don\u2019t try working with $sin(x+y)$ and $sin (x-y)$. Instead, use $sin(X+Y) = sin(x)cos(y)+cos(x)sin(y)$ so that all the angles match<\/p>\n\n\n\n

      (2) Converting to sin and cos all the items in the problem using a basic formula. I have mentioned sin and cos as they are easy to solve. You can use any other also.<\/p>\n\n\n\n

      (3)Check all the angles for sums and differences and use the appropriate identities to remove them.<\/p>\n\n\n\n

      (4) Use Pythagorean identifies  to simplify the equations<\/p>\n\n\n\n

      (5) Practice and Practice. You will soon start figuring out the equation and their symmetry to resolve them fast<\/p>\n\n\n\n

      Download all the trigonometry Formulas below<\/p>\n\n\n\n

      Hope you like this compilation of Trigonometry Formulas for class 11. This will be very useful for the Maths students<\/p>\n\n\n\n

      Download Trigonometry Formulas PDF<\/h2>\n\n\n\n