- #1
courtrigrad
- 1,236
- 2
Hello all
Just came across a few questions on related rates and would like some verification on whether I am doing these correctly:
1. Let [tex] \theta [/tex] be an acute angle in a right triangle, and let x and y, respectively be the sides adjacent and opposite of [tex] \theta [/tex]. Suppose that x and y vary with time? How are [tex] \frac{d\theta}{dt} \frac{dx}{dt} \frac{dy}{dt} [/tex] related? Well I set up a relationship where [tex] tan \theta = \frac{y}{x} [/tex] So [tex] \theta = \arctan(\frac{y}{x}) [/tex] Hence [tex]\frac{d\theta}{dt} = d(\arctan(\frac{y}{x}) [/tex] Is this right?
Just came across a few questions on related rates and would like some verification on whether I am doing these correctly:
1. Let [tex] \theta [/tex] be an acute angle in a right triangle, and let x and y, respectively be the sides adjacent and opposite of [tex] \theta [/tex]. Suppose that x and y vary with time? How are [tex] \frac{d\theta}{dt} \frac{dx}{dt} \frac{dy}{dt} [/tex] related? Well I set up a relationship where [tex] tan \theta = \frac{y}{x} [/tex] So [tex] \theta = \arctan(\frac{y}{x}) [/tex] Hence [tex]\frac{d\theta}{dt} = d(\arctan(\frac{y}{x}) [/tex] Is this right?