Question

This table shows some of the values of x and y that satisfy the equation y=acos0+b, find the value of y when x = 45

Answer 1

Answer:
`4√(2)+1`

Explanation:

`x=0 \implies y=a+b \implies a+b=9\\\\x=30 \implies (√(3))/(2)a+b=1+4√(3)\\\\\implies (√(3))/(2)a-a=4√(3)-8\\\\a=(4√(3)-8)/((√(3))/(2)-1)=(8√(3)-16)/(√(3)-2)=8\\\\\implies b=9-8=1\\\\\therefore y=8\cos x^(\circ)+1\\\\x=45 \implies y=8\left((√(2))/(2) \right)+1=4√(2)+1`