A curve has the equation

\sin x + b \cos x

where $a\,$ and $b\,$ are constants.

The maximum value of $y\,$ is 4 and the curve passes through the point $(π4,4)\displaystyle \left(\frac{\pi}{4}, 4\right)$

Show that $a^2+b^2=16$ .

Hence find, to 3 decimal places, the values of $a\,$ and $b$ .

A curve has the equation

\sin x + b \cos x

where $a\,$ and $b\,$ are constants.

The maximum value of $y\,$ is 4 and the curve passes through the point $(π4,4)\displaystyle \left(\frac{\pi}{4}, 4\right)$

Show that $a^2+b^2=16$ .

Hence find, to 3 decimal places, the values of $a\,$ and $b$ .

Trigonometry and Modelling

Trigonometry and Modelling Questions