1 / 19

Inverse Trigonometric Functions

Inverse Trigonometric Functions. Properties and Formulae. ANIL SHARMA K.V. HIRA NAGAR. we have studied that the inverse of a function f, denoted by f –1, exists if f is one-one and onto. There are many functions which are not one-one, onto or both and

nodin
Télécharger la présentation

Inverse Trigonometric Functions

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Inverse Trigonometric Functions Properties and Formulae ANIL SHARMA K.V. HIRA NAGAR

  2. we have studied that the inverse of a function f, denoted by f –1, exists if f is one-one and onto. There are many functions which are not one-one, onto or both and hence we can not talk of their inversesThe concepts of inverse trigonometric functions is also used in science and engineering we have studied that the inverse of a function f, denoted by f –1, exists if f is one-one and onto. There are many functions which are not one-one, onto or both and hence we can not talk of their inverses.

  3. Pretesting Questions:- Q 1) Can you suggest the restricted Domains of each T ratios separately at which the functions are one and onto ? Q2) When a function is said to be invertible. ? Q3 Evaluate the followings a) Sin-1(1/2) b) Sin-1(-1/2) c) Tan-1(1) d) Sin-1(2sin∏/6) Q4) If Sin-1( x-1) =∏/4 then find the value of x.

  4. Inverse Trigonometric function – Properties sin-1 (-x) = -sin-1 (x) if x is in [-1,1] cos-1 (-x) = - cos-1x if x is in [-1,1] tan-1(-x) = - tan-1x if x is in ( -, ) cot-1(-x) =  - cot-1x if x is in (-,) cosec-1(-x) = - cosec-1x if x is in (-,-1] U [1,) sec-1(-x) =  - sec-1x if x is in (-,-1] U [1,)

  5. Other important properties sin-1 x+ cos-1 x = /2 ; if x is in [-1,1] If x > 0 , y > 0 and xy < 1 If x<0,y<0 and xy < 1 If x > 0 , y > 0 and xy > 1

  6. Find the value of Solution :

  7. sin-1 x+ cos-1 x = /2 ; if x is in [-1,1] If x > 0 , y > 0 and xy < 1 If x<0,y<0 and xy < 1 If x > 0 , y > 0 and xy > 1 Other important properties

  8. Prove that Solution : And L.H.S. of the given identity is +

  9. In triangle ABC if A = tan-12 and B = tan-1 3 , prove that C = 450 Solution : For triangle ABC , A+B+C = 

  10. Inverse Trigonometric function – Conversion To convert one inverse function to other inverse function : • Assume given inverse function as some angle ( say  ) • Draw a right angled triangle satisfying the angle. Find the third un known side • Find the trigonometric function from the triangle in step 2. Take its inverse and we will get  = desired inverse function

  11. The value of cot-1 3 + cosec-1 5 is (a) /3 (b) /2 ( c) /4 (d) none Step 1 Assume given inverse function as some angle ( say  ) Letcot-1 3 + cosec-1 5 = x + y, Where x = cot-13 ; cot x = 3 and y = cosec-1  5 ; cosec y =  5

  12. If sin-1 x + sin-1 (1- x) = cos-1x, the value of x could be (a) 1, 0 (b) 1,1/2 (c) 0,1/2 (d) 1, -1/2 Solution :

  13. If cos-1 x + cos-1 y + cos-1z = , Then prove that x2+y2+z2 = 1 - 2xyz Solution : and given : A+B+C =  Now, L.H.S. = cos2A + cos2B +cos2C = cos2A + 1- sin2B +cos2C = 1+(cos2A - sin2B) +cos2C

More Related