# if $\theta$ increases at a constant rate of 3 rads per min, at what rate is x increasing in units per min when x = 3 units?

In triangle shown above, if $\theta$ increases at a constant rate of 3 radians per minute, at what rate is $x$ increasing in units per minute when $x$ equals $3$ units?

• Do you know how to set up related rates problems or implicit differentiation? – turkeyhundt Dec 8 '14 at 3:42
• yes we are supposed to use related rates – lemonadedoge Dec 8 '14 at 3:43
• i did $5cos(\theta)\theta'=x'$ – lemonadedoge Dec 8 '14 at 3:44
• Plug in what you know. You know $\theta '$ is 3, and you should be able to find $\theta$ since it's a right triangle and you know two sides (5 and 3) – turkeyhundt Dec 8 '14 at 3:46

you can use the constraint $$x = 5 \sin \theta, \to \frac{dx}{dt} = 5\cos \theta \frac{d\theta}{dt} = 15 \cos \theta = 15 \times \frac 4 5=12 \, unit/min$$
$$\theta =\arcsin(3/5)$$
$$x'=5\cos(\arcsin(3/5))\cdot3$$
$$x'=12 \text{ units/min}$$