# Trigonometric equations with sin and cot

• dbg11
In summary, the problem asks to find the value of cot(2sin^(-1) 2/7). The attempt at a solution involved solving for sine by drawing a unit circle and using the given values of 2 for the y value and 7 for the r value (hypotenuse). However, the x value was incorrectly calculated as 4 sqrt(3), when it should be 3√5. This resulted in an incorrect answer for the cotangent value. The issue may have been caused by the (2 sin) in the equation.
dbg11

## Homework Statement

find the value(s): cot(2sin^(-1) 2/7)

## The Attempt at a Solution

I solved for sine by drawing a unit circle and the angle. I used the given values of 2 for the y value and 7 for the r value(hypotenuse). By using the pythagorean theorem I found the x value which, for me, came out to 4 sqrt(3). From the x value I was able to find the cosine. Since cotangeant is cosine/ sine I solved for that to get my exact value but it did not come out to the correct answer.
I think it had something to do with the (2 sin) in the equation. I am not sure exactly what to do when an equation gives me a number times sine.

Last edited by a moderator:
$\frac{1}{tan(\frac{2}{sin(2/7)})}$ ?

dbg11 said:

## Homework Statement

find the value(s): cot(2sin^(-1) 2/7)

## The Attempt at a Solution

I solved for sine by drawing a unit circle and the angle. I used the given values of 2 for the y value and 7 for the r value(hypotenuse). By using the pythagorean theorem I found the x value which, for me, came out to 4 sqrt(3).
I get 3√5, not 4√3.
dbg11 said:
From the x value I was able to find the cosine. Since cotangeant is cosine/ sine I solved for that to get my exact value but it did not come out to the correct answer.
I think it had something to do with the (2 sin) in the equation. I am not sure exactly what to do when an equation gives me a number times sine.

## 1. What are trigonometric equations with sin and cot?

Trigonometric equations with sin and cot involve using the sine and cotangent functions to solve for unknown angles or side lengths in a triangle. These equations can also involve manipulating the equations to find solutions in terms of trigonometric identities.

## 2. How do I solve trigonometric equations with sin and cot?

To solve these equations, you can use algebraic manipulation, trigonometric identities, and/or the unit circle. It is important to also keep track of the domain and range of the solutions and to check for extraneous solutions that may arise.

## 3. What are some common strategies for solving trigonometric equations with sin and cot?

Some common strategies include using the reciprocal identities for sine and cotangent, simplifying the equations using trigonometric identities, and substituting known values from the unit circle to find solutions.

## 4. Are there any special cases when solving trigonometric equations with sin and cot?

Yes, there are special cases when solving these equations. These include when the equation involves a double angle, half angle, or sum/difference of angles. It is important to be familiar with these special cases and the corresponding identities.

## 5. How can I check my solutions for trigonometric equations with sin and cot?

You can check your solutions by plugging them back into the original equation and verifying that the equation holds true. You can also graph the equations to see if the solutions match the points of intersection on the graph.

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