evaluate cos(inverse)1/2

Question

evaluate arccos1/2.

 

 

MY ANSWER: 1.047

 

HOW MANY SOLUTIONS DOES ARCCOS0 HAVE??

 

???

 

EVALUATE COT{ARCCOS((-15/17))}  WRITE AS FRACTION

 

 

THE VALUE ∏/12 IS A SOLUTION FOR 4COS^2(4X)-3=0

TRUE OR FALSE

 

 

Answer 1

y = cos^-1(1/2) = π/3 and, since the cos is also positive for (3π/2, 2π), the answer needs to include 5π/3.

 

The value of arccos0 has two values:  at π/2, and 3π/2.

 

Arccos(-15/17):  x = -15, r = 17, and y = 8.  Therefore, the cot must = x/y, or -15/8.

 

If 4cos²(4x) - 3 = 0 and x = π/12, 4cos²(4x) - 3 = 4cos²(π/3) - 3 = 4(½)² - 3 = 4(¼) - 3 = 1 - 3 = -2.

 

Therefore, I'd say "false".