Using the equation given :

x=5 sec `theta`

sketch the corresponding right angle triangle's diagram and give the value of the remaining trigonometric functions for any value of x.

(inroductions of trignometric functions in calculus)

### 1 Answer | Add Yours

Let consider a right angle triangle ABC, right angle at C.Also let angle A is equal to theta.Then

`sec(theta)=(AB)/(AC)=x/5`

`also`

`AB^2=AC^2+BC^2` ( BY Pythagoras Theorem)

ie.

`x^2=5^2+BC^2`

`BC^2=x^2-25`

`BC=sqrt(x^2-25)`

`sin(theta)=(BC)/(AB)=sqrt(x^2-25)/x`

`cos(theta)=1/(sec(theta))=5/x`

`tan(theta)=sqrt(x^2-25)/5`

`cot(theta)=1/(tan(theta))=5/sqrt(x^2-25)`

`cosec(theta)=1/(sin(theta))=x/sqrt(x^2-25)`

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