Question 1164806: Solve for theta:sin-sec+csn-tan2=-0.0866
Answer by CPhill(2189)   (Show Source):
You can put this solution on YOUR website! It appears there are a few typos in your expression. Based on standard trigonometric shorthand, I will interpret your equation as:
If "csn" was meant to be **** and "tan2" meant ****, we can solve it as follows:
### 1. Simplify the Trigonometric Terms
First, let's rewrite everything in terms of and to see if the expression simplifies.
*
*
Now, substitute these back into the equation:
### 2. Find a Common Denominator
Since , the equation becomes:
### 3. Solve for
This is a transcendental equation, which usually requires numerical methods or a graphing calculator to solve precisely. However, we can test small values since is close to zero.
If we let :
* If , then .
* Since the result is slightly negative (), must be a small negative angle.
Using the small-angle approximation where and :
Using the quadratic formula :
### 4. Convert to Degrees
Checking this in the original equation:
(Very close to ).
**Solution:**
*(Note: If the "tan2" in your prompt meant or if "csn" meant something else, the solution would change.)*
**Would you like me to re-calculate this using a different interpretation of the symbols?**
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