Conical pendulum: what are the tension and the angle?

[pkc111]

Homework Statement:

A rock with a mass 1.5 kg is being whirled in a horizontal circle on a string 0.8 m long. The speed of the rock is a constant 5 m/s. Find the magnitude and direction of the tension in the string.
COMMENT: There seems to be too many unknowns here.

Relevant Equations:

Fc = mv2/r
W = mg

 

[haruspex]

Homework Statement:: A rock with a mass 1.5 kg is being whirled in a horizontal circle on a string 0.8 m long. The speed of the rock is a constant 5 m/s. Find the magnitude and direction of the tension in the string.
COMMENT: There seems to be too many unknowns here.
Relevant Equations:: Fc = mv2/r
W = mg

View attachment 259616View attachment 259617

So what is cos²(θ) in terms of sin(θ)?

By the way, it is far better style to keep everything algebraic. Don't plug in numbers until the end. For one thing, more people will take the trouble to check your work.

 

[pkc111]

Thank you for your reply.
Are you saying that this question is solvable with the information provided in the question?

 

[pkc111]

Cos my gut feeling is the question is wrongly written ..as every other question in this high school physics textbook chapter needs only very straightforward maths...Is someone able to say whether the information is enough to define a specific conic pendulum case which is solvable?

 

[haruspex]

Thank you for your reply.
Are you saying that this question is solvable with the information provided in the question?

In your last equation in post #1 there is only one unknown, so it should be solvable.
I repeat, what equation relates sin to cos (and involves no other trig function)?