Which of the following?

Question

Which of the following gives the Taylor polynomial of order 5 approximation to sin(1.5)?

 

a) 0.965

b) 0.985

c) 0.997

d) 1.001

e) 1.005

 

Please show all your work. 

Answer 1

sin(x)=x-x³/6+x⁵/120+o(x⁵); 

 

Substitution gives:

 

sin(1.5)≈1.00078≈1.001

 

Answer is d)