Question

From the following figure,find the values of:
(i) cos A
(ii) cosec A
(iii) tan^2 A- sec^2 A
(iv) sin C
(v) sec C
(vi) cot^2 C - 1/sin^2 C​

Answer 1

Answer:

It has given that, In an experiment to measure the diameter of a wire as measured by a screw gauge was found to be 0.026 cm, 0.028 cm, 0.027 cm, 0.024 cm, 0.027 cm, 0.029 cm.

To find :

mean value of the diameter

mean absolute error

relative error

percentage error of the above measurements.

solutiom : Observations are : 0.026 , 0.028, 0.027, 0.024, 0.027 , 0.029

Mean = sum of observations/number of observations

= (0.026 + 0.028 + 0.027 + 0.024 + 0.027 + 0.029)/6

= 0.0268 ≈ 0.027 cm

∴ mean value = 0.027 cm

Now, y₁ =|0.026 - 0.027| = 0.001

y₂ = |0.028 - 0.027| = 0.001

y₃ = |0.027 - 0.027| = 0.000

y₄ = |0.024 - 0.027| = 0.003

y₅ = |0.027 - 0.027| = 0.000

y₆ = |0.029 - 0.027| = 0.002

Now, absolue error ,∆y = (y₁ + y₂ + y₃ + y₄ + y₅ + y₆)/6

= (0.001 + 0.001 + 0.000 + 0.003 + 0.000 + 0.002)/6

= 0.007/6

= 0.00116

Now, relative error = absolute error/mean value

= 0.00116/0.027

= 0.04296

percentage error = relative error × 100

= 0.04296 × 100 = 4.296 ≈ 4.3 %