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math-formula-sheet-trigonometry

In this "math-formula-sheet-trigonometry" I am going to provide almost all formula regarding this, which helps "College Grade" and as well as "10th " to "12th "Grade students to solve "trigonometric problems" easily.

First let us go through basic formula of Trigonometry.

We know that when right triangle is given , to find sine, cosine, tangent the easy way to remember is SOHCAHTOA .

SOH stands for "Sine angle" which is the ratio of "Opposite side" to" Hypotenuse ".

Similarly CAH stands for "Cosine angle" which is the ratio of "Adjacent side to Hypotenuse".

TOA stands for "Tangent angle" which is the ratio of "Opposite side to Adjacent side".

Other three are reciprocals of these three.

"math-formula-sheet-trigonometry"

1) Sin\(\Theta\)=\(\frac{Opp}{Hyp}\)

2) Cos\(\Theta\)=\(\frac{Adj}{Hyp}\)

3) Tan\(\Theta\)=\(\frac{Opp}{Adj}\)

4) Cot\(\Theta\)=\(\frac{1}{Tan\Theta}=\frac{Adj}{Opp}\)

5) Sec\(\Theta\)=\(\frac{1}{Cos\Theta}=\frac{Hyp}{Adj}\)

6) Csc\(\Theta\)=\(\frac{1}{Sin\Theta}=\frac{Hyp}{Opp}\)

II Identities : "math-formula-sheet-trigonometry"

1) \(Cos^{2}x + Sin^{2}x=1\)

2)\(Sec^{2}x - Tan^{2}x =1\)

3)\(Csc^{2}x - Cot^{2}x =1\)

Their derivatives are

1)\(Cos^{2}x + Sin^{2}x=1\)

    a) \(Cos^{2}x= 1 -Sin^{2}x\)

    b) \(Sin^{2}x= 1 -Cos^{2}x\)

    c)Cos(x)= \(\sqrt{1-Sin^{2}x}\)

     d) Sin(x) =\(\sqrt{1-Cos^{2}x}\)

2) \(Sec^{2}x - Tan^{2}x =1\)

  a) (Sec(x) + Tan(x))*(Sec(x) - Tan(x))=1

   b) Sec(x) + Tan(x) =\(\frac{1}{Sec(x) - Tan(x)}\)

   c)Sec(x) - Tan(x)=\(\frac{1}{Sec(x) + Tan(x)}\)

   d) \(Sec^{2}x=1+Tan^{2}x\)

    e) Sec(x)=\(\sqrt{1+Tan^{2}x}\)

    f)\(Tan^{2}x=Sec^{2}x - 1\)

    g) Tan(x)=\(\sqrt{Sec^{2}x - 1}\)

3) \(Csc^{2}x - Cot^{2}x =1\)

  a) (Csc(x) + Cot(x))*(Csc(x) - Cot(x))=1

   b) Csc(x) + Cot(x) =\(\frac{1}{Csc(x) - Cot(x)}\)

   c) Csc(x) - Cot(x)=\(\frac{1}{Csc(x) + Cot(x)}\)

   d) \(Csc^{2}x=1+Cot^{2}x\)

    e) Csc(x)=\(\sqrt{1+Cot^{2}x}\)

    f)\(Cot^{2}x=Csc^{2}x - 1\)

    g) Cot(x)=\(\sqrt{Csc^{2}x - 1}\)

III.

 1) Sin(x) * Csc(x)=1

  2) Cos(x)* Sec(x)=1

  3) Tan(x) * Cot(x)=1

In next page you can see the formula of sum and difference of trigonometric ratios Sin, Cos, Tan and Cot .


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