3.8 Solving trigonometric equations questions for IB Maths AA

Find the coordinates of the bead when $t=2.5$.

Find the value of $t$ when the bead first returns to its starting position.

Find the values of $t$ for which the $x$-coordinate of the bead is $-0.6$ and its $y$-coordinate is positive.

Find the exact height of the seat when $t=9$.

Write down the maximum height of the seat and the value of $t$ at which it occurs.

Find the values of $t$ for which $h(t)=29$.

Hence, find the length of time during one revolution for which the seat is more than 29 m above the ground.

Find the rate at which the height of the seat is changing when $t=2$.

Find the values of $t$ at which the seat is descending at a rate of ${\displaystyle \frac{3\pi }{4}}$ metres per minute.

Show that the equation can be written as $3{\sin }^{2}x+2\sin x-1=0$.

Hence, solve the equation $3\cos 2x=4\sin x+1$, for $0\le x\le 2\pi$.

Show that $f(x)=1-\sin 2x$.

Hence, solve $f(x)={\displaystyle \frac{3}{2}}$, for $0\le x\le \pi$.

Express $f(x)$ in the form $a\sin (bx)$, where $a,b\in {\mathbb{Z}}^{+}$.

Write down the period of $f$.

Write down the range of $f$.

Solve the equation $f(x)=1.8$.