New Zealand
Level 8 - NCEA Level 3

# Area between two sin/cos curves

## Interactive practice questions

Find the area bound by the curves $y=\sin2x$y=sin2x and $y=\cos x$y=cosx over the domain $\frac{\pi}{6}\le x\le\frac{\pi}{2}$π6xπ2.

(Note that we are interested in the area bounded by the two curves, not one curve and an axis.)

Easy
Approx 4 minutes

Find the area enclosed by the curves $y=\sin x$y=sinx and $y=\cos x$y=cosx, and the lines $x=0$x=0 and $x=\frac{\pi}{4}$x=π4.

The figure shows the area bound by the curves $y=4\cos x$y=4cosx, $y=-4\cos\left(x-\frac{\pi}{2}\right)$y=4cos(xπ2), the $y$y-axis and $x=\frac{3\pi}{4}$x=3π4.

The two functions $y=5\cos2x$y=5cos2x and $y=5\sin\left(\frac{x}{2}\right)$y=5sin(x2) meet at $x=\frac{\pi}{5}$x=π5 and $x=\pi$x=π.

Find the area bounded by the two curves. Give your answer to two decimal places.

### Outcomes

#### M8-11

Choose and apply a variety of differentiation, integration, and antidifferentiation techniques to functions and relations, using both analytical and numerical methods

#### 91579

Apply integration methods in solving problems