What is the angle needed to solve for the shopping cart problem?

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To solve for the angle in the shopping cart problem involving a ramp, the equations 0.17 = 0.1 cos x and 0.1 cos x = sin x are used. The first equation leads to an impossible scenario, as it suggests x = cos-1(1.7), which is undefined since the cosine function cannot exceed 1. The second equation provides x = tan-1(0.1), which is a valid angle. The discussion emphasizes the importance of ensuring that both equations yield the same angle, indicating a potential error if they do not. Understanding the constraints of trigonometric functions is crucial in resolving the problem.
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alright this question involved a shopping cart up a ramp with an unknown angle and i have all the other variables but, cannot find the angle

.17 = .1cosx = sinx i need angle x, simple trig i believe but, i can't do it
 
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Based on 0.17 = 0.1 cos x,

the x = cos-1 1.7

Based on 0.1 cos x = sin x,

x = tan-1 0.1


If one has developed the correct relationships, the x from either equation should be the same. If not there is something wrong.
 
Astronuc said:
Based on 0.17 = 0.1 cos x,
the x = cos-1 1.7
Just added to what Astronuc had said:
Since you have:
\forall x \in \mathbb{R}, \ \ \nexists x \ | \ \ \ |\cos x| > 1
So, what can you say about x?
Viet Dao,
 

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