Loading....
Coupon Accepted Successfully!

 

Trigonometric Ratios

In a right-angled triangle ABC.
 Let,  AB = p
        BC = b
        AC = h


We define the six trigonometrical ratios as shown under,

sin

θ = Sine θ =
cos
θ = cosine q =
tan
θ  = tangent θ =
cosecant
θ = cosec θ =
secant
θ = sec θ =
cotangent
θ = cot θ

Note 1
From the above definitions we observe that,
cosec
θ = , sec θ = , cot θ =

Note 2
cosec
θ is defined when sin θ ≠ θ, sec θ is defined when cos θ ≠ 0 and cot θ is defined when
tan
θ ≠ 0.

Note 3
Maximum value of sin
θ = 1 when θ = 90°, Maximum value of cos θ = 1 when θ = 0 and the maximum value of tan θ is not defined.

Problem 1:

 
Example
  Find the values of sec A and cot A, if tan C =
Solution
Consider a Δ ABC, right angled at B,

 

As it is given that, tan C = .

Therefore, if , where k is a positive number.

Now, by using the Pythagoras theorem,

Using the definitions of trigonometric ratios we have to find the values of sec A and cot A.

Thus sec A = and cot A = .

 
 
 




Test Your Skills Now!
Take a Quiz now
Reviewer Name