Solve Cosecant

Introduction to solve cosecant:

In trigonometry functions we study about the trigonometry terms to find weather the value of the right angle or any angle of the right angle triangle is found. These values are study through the trig terms like sine (sin), cos (cosine) and tan (tangent). We also have inverse trigonometry functions for sine as cosecant, cosine as secant and tangent as cotangent . By using solve trig terms we can solve the trigonometry terms and find the accurate values. Let us study about trig terms with some examples.

Formulas for Trigonometric Functions:

1. `sin^2theta + cos^2theta =1`

2.  `sin 2theta` = `2 sin theta cos theta`

3. `cos 2theta` =` 1 - 2 sin^2 theta`

4. `""1/(sec theta)` = `cos theta`

5. `sin (-theta)` = `- sin theta`

6. `" cos ` = `cos theta`

7.  `"e^(+-jtheta) ` = `cos theta`   ± `j sin theta`

8.` 1 + tan^2 theta ` = `sec^2 theta`

9.` tan (a +- b)` = `(tan a +- tan b)/(1+- tana tan b) `


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Solve Cosecant Problems:

Solve cosecant problem 1:

Solve trigonometric equation :  4 cosec x - 8 = 0

Solution:

Given trigonometric equation is  4 cosec x - 8 = 0

Add  by 8 on both sides.we get

4 cosecx - 8+ 8 = 8

4 cosecx = 8

Now, Both sides divided by 4. so we get the equation is

`(4cosec x)/4` = `8/4` .= 2

cosec x = 2.

So, x = cose-1 2 .

x = `(pi/6)` .

But the cosec term is positive in First and second quadrants. so , cosec`(pi - pi/6)` = cosec `((5pi)/6)`.

and   sin`((5pi)/6)` = 2 .

So, The solutions are . x = `(pi/6)`and x = `((5pi)/6)`

Solve cosecant problem 2:

Solve trigonometric equation :  5cosec x - 5 = 0

Solution:

Given trigonometric equation is  5cosec x - 5 = 0

Add  by 5 on both sides.we get

5 cosecx - 5+ 5 =5

5 cosecx = 5

Now, Both sides divided by 5. so we get the equation is

`(5cosec x)/5` = `5/5` .= 1

cosec x = 1.

So, x = cose-1 1 .

x = `(pi/2)`

So, The value of x = `(pi/2)` .