(Sin^3)/cos??????

[Kamhogo]

Hello,

I am given [Sin^2 (theta)]/[cos (theta)] = 911,9635 x 10 ^9. I don't even how to start solving rid.
I've liked for trigonometric identities but the solution to/simplification of sin^3/cos is
nowhere to be found. Can someone help? Thanks!

 

[Haymedoots]

Hello,

I am given [Sin^2 (theta)]/[cos (theta)] = 911,9635 x 10 ^9. I don't even how to start solving rid.
I've liked for trigonometric identities but the solution to/simplification of sin^3/cos is
nowhere to be found. Can someone help? Thanks!

What identity relates sin^2(theta) to cos(theta)?

Is 911,9635 x 10^9 an error?

 

[Deleted member 4993]

Hello,

I am given [Sin^2 (theta)]/[cos (theta)] = 911,9635 x 10 ^9. I don't even how to start solving rid.
I've liked for trigonometric identities but the solution to/simplification of sin^3/cos is
nowhere to be found. Can someone help? Thanks!

What is the exponent of sin(Θ) - 2 or 3?

 

[Kamhogo]

Sorry for the typo, it's sin^3

 

[Kamhogo]

What identity relates sin^2(theta) to cos(theta)?

Is 911,9635 x 10^9 an error?

Yes it is. It's actually 911.9635 x 10^(-9)

Context :

Right triangle.
Base Tx = (18611.5 *10^(-9))/sin^2(theta)
Right side Ty = 0.049
Theta is the angle between the hypotenuse T and Ty or the angle opposite Tx.
Tan ( theta ) = Tx/Ty
= [{(18611.5*10^(-9))/sin^2 (theta)}/0.049]
= ( 911.9635*10^(-9))/sin^2 (theta)
Sin (theta)/cos (theta) = (911.9635*10^(-9))/sin^2 (theta)

= => 911.9635*10^(-9)= sin^3 (theta)/cos (theta )

Find theta. The answer is 4.1 degrees but I'd like to know how to get there.

 

[Kamhogo]

 

[Deleted member 4993]

Yes it is. It's actually 911.9635 x 10^(-9)

Context :

Right triangle.
Base Tx = (18611.5 *10^(-9))/sin^2(theta)
Right side Ty = 0.049
Theta is the angle between the hypotenuse T and Ty or the angle opposite Tx.
Tan ( theta ) = Tx/Ty
= [{(18611.5*10^(-9))/sin^2 (theta)}/0.049]
= ( 911.9635*10^(-9))/sin^2 (theta)
Sin (theta)/cos (theta) = (911.9635*10^(-9))/sin^2 (theta)

= => 911.9635*10^(-9)= sin^3 (theta)/cos (theta )

Find theta. The answer is 4.1 degrees but I'd like to know how to get there.

That number is too small for the expected answer. For the expected angle to be correct - that constant should be ~ 367 * 10^(-6)

For the given constant - the angle is ~0.556°

You can check these by using these values into your equation.

 

[Ishuda]

Hello,

I am given [Sin^2 (theta)]/[cos (theta)] = 911,9635 x 10 ^9. I don't even how to start solving rid.
I've liked for trigonometric identities but the solution to/simplification of sin^3/cos is
nowhere to be found. Can someone help? Thanks!

To make it easy let
a = the constant,
s = sin(\(\displaystyle \theta\)),
c = cos(\(\displaystyle \theta\))
and n the exponent on the sine function.
Then the expression becomes
\(\displaystyle \frac{s^n}{c}\, =\, \frac{[1-c^2]^{\frac{n}{2}}}{c}\, =\, a\)
or squaring both sides
\(\displaystyle \frac{[1-c^2]^n}{c^2}\, =\, a^2\)
which just means finding the roots of an nth degree equation of a polynomial in c² of degree n. Since a is so large in this case, I would suggest dividing through by a².