Help with 45° Angle Equation Solving

[chemic_23]

Homework Statement

i can't think of any equation to plug the 45 degrees angle pls help... i tried

D_ttanθ=y/x

(secθ)^2)(dθ/dt)=[x(dy/dt)-y(dx/dt)]/x^2

but i don't know the value of x when tanθ=45 degrees... do i need to set my calcu to radians or just in degrees mode then i get tanθ=y/x ---> tan45=y/x

1=y/x
x=y

 

[nicksauce]

but i don't know the value of x when tanθ=45 degrees

.
First, it's θ=45 not tanθ=45. Second, if θ=45 what is the relationship between x and y? Using this relationship and x = 10 + 2t, y = 6 + 4t, can you find x and y when θ=45?

i can't think of any equation to plug the 45 degrees angle pls help

How about putting it in for that secθ you have in
(secθ)^2)(dθ/dt)=[x(dy/dt)-y(dx/dt)]/x^2?

 

[chemic_23]

awww sorry hehe mistyped. it's tan45 hehe
i came up with this solution
x=10+2t
y=6+4t

tan45=(6+4t)/(10+2t) (deg mode)
1=(6+4t)/(10+2t)
10+2t=6+4t
t=2

substituting in (secθ)^2)(dθ/dt)=[x(dy/dt)-y(dx/dt)]/x^2
i got ((cos45)^2)/7 per sec or 1/14 per sec
is this correct? or should i set my calculator in radian mode?

 

[HallsofIvy]

d(sin x)/dx = cos x and d(cos x)/dx= -sin x ONLY if x is in radians. Those formulas are not valid if the angle is not in radians.