Basic derivatives of sine and cosine
Interactive practice questions
Consider the graph of $y=\sin x$y=sinx.
Which of the following best describes the graph of $y=\sin x$y=sinx?
It is constantly increasing.
It is constantly decreasing.
The graph increases and decreases periodically.
Which of the following best describes the nature of the gradient of the curve?
Select all the correct options.
Between points where the gradient is $0$0, the gradient is always negative.
The gradient of the curve is $0$0 once every $2\pi$2π radians.
Between points where the gradient is $0$0, the gradient is always positive.
The gradient of the curve is $0$0 once every $\pi$π radians.
Between points where the gradient is $0$0, the gradient is positive and negative alternately.
Select all the intervals in which the gradient of $y=\sin x$y=sinx is positive.
$\frac{\pi}{2}
$\pi\le x<\frac{3\pi}{2}$π≤x<3π2
$\frac{3\pi}{2}
$0\le x<\frac{\pi}{2}$0≤x<π2
Select all the intervals in which the gradient of $y=\sin x$y=sinx is negative.
$\frac{3\pi}{2}
$0\le x<\frac{\pi}{2}$0≤x<π2
$\frac{\pi}{2}
$\pi\le x<\frac{3\pi}{2}$π≤x<3π2
The gradient function $y'$y′ is to be graphed on the axes below. The plotted points correspond to where the gradient of $y=\sin x$y=sinx is $0$0.
Given that the gradient at $0$0 is $1$1, graph the gradient function $y'$y′.
Which of the following is the equation of the gradient function $y'$y′ graphed in the previous part?
$y'=-\cos x$y′=−cosx
$y'=-\sin x$y′=−sinx
$y'=\sin x$y′=sinx
$y'=\cos x$y′=cosx
Consider the graph of $y=\cos x$y=cosx.
Consider the graphs of $y=\sin x$y=sinx and its derivative $y'=\cos x$y′=cosx below. A number of points have been labelled on the graph of $y'=\cos x$y′=cosx.
Consider the graphs of $y=\cos x$y=cosx and its derivative $y'=-\sin x$y′=−sinx below. A number of points have been labelled on the graph of $y'=-\sin x$y′=−sinx.