# Thread: sine inverse and theta value

1. ## sine inverse and theta value

is it possible to find the value of x in $\displaystyle sin x = \frac {\sqrt {5}-1}{4}$ without a calculator?

another question..

find the value of theta if $\displaystyle cos(2 \theta)-sin(\theta)=\theta$

also ..

find the length of the hypotenuse in a right triangle if the sum of its three sides is 200.

2. Originally Posted by eq123
is it possible to find the value of x in $\displaystyle sin x = \frac {\sqrt {5}-1}{4}$ without a calculator?

another question..

find the value of theta if $\displaystyle cos(2 \theta)-sin(\theta)=\theta$

also ..

find the length of the hypotenuse in a right triangle if the sum of its three sides is 200.
Please provide some context for these (that is on what part of your course did they arise and what course for that matter).

CB

3. these problems are not related to the study of a specific course.. they are just some problems that i find interesting..

4. Originally Posted by eq123
these problems are not related to the study of a specific course.. they are just some problems that i find interesting..
Then they are not trigonometry, and I will move them; I think to the Calculus forum.

CB

5. Originally Posted by eq123
is it possible to find the value of x in $\displaystyle sin x = \frac {\sqrt {5}-1}{4}$ without a calculator?

another question..

find the value of theta if $\displaystyle cos(2 \theta)-sin(\theta)=\theta$

also ..

find the length of the hypotenuse in a right triangle if the sum of its three sides is 200.
The first two you will need to find the roots numerically.

CB

6. i don't think that these problems are related to calculus..

anyway, can you provide any additional information?

7. Originally Posted by eq123
i don't think that these problems are related to calculus..

anyway, can you provide any additional information?
Google for "numerical solution of non-linear equations", "Newton Raphson" and/or "bisection algorithm"

CB

8. i am still trying to figure out the solution for these problems .. especially for the question $\displaystyle cos(2 \theta)-sin(\theta)=\theta$ .. i would appreciate it if anyone can provide a step by step solution..

9. Originally Posted by eq123
i am still trying to figure out the solution for these problems .. especially for the question $\displaystyle cos(2 \theta)-sin(\theta)=\theta$ .. i would appreciate it if anyone can provide a step by step solution..
This almost certainly has a solution which cannot be expressed in closed form using elementary functions and well known constants.

Sketch the curve $\displaystyle y=\cos(2 \theta)-\sin(\theta)-\theta$ and it is obvious that it has a single root between 0 and 1. The using the Bisection or NR algorithms you will find that the root is $\displaystyle \approx 0.372087$

CB

10. thank you. i was able to find the solution using newton raphson method.