mathmath333 one year ago Trignometry question

1. mathmath333

\large \color{black}{\begin{align} & x\cos \theta -\sin \theta =1 \hspace{.33em}\\~\\ & x^{2}+(1+x^{2})\sin \theta \ \text{equals} \hspace{.33em}\\~\\ & a.)\ 0 \hspace{.33em}\\~\\ & b.)\ 2 \hspace{.33em}\\~\\ & c.)\ 1 \hspace{.33em}\\~\\ & d.)\ -1 \hspace{.33em}\\~\\ \end{align}}

2. phi

one thought is to set theta to a particular value. for example let theta=0 (the idea is if w have an identity, it works for all values of theta) using that idea, from the first equation x cos theta - sin theta = 1 x = 1 and x=1 in the 2nd equation gives 1

3. mathmath333

is this question has to solved in 1 min there must be a trick here

4. mathmath333

beside $$\theta =0$$

5. phi

your answer choices are all numbers. that suggests the answer is independent of theta (otherwise we would have choices that are expressions with theta) so if theta does not matter, pick a value that is easy to evaluate.

6. mathmath333

ok

7. phi

unfortunately, if we solve for x using the first equation x= (1+ sin A)/ cos A and plug that into the 2nd equation, we get a messy trig function wolfram can plot it. http://www.wolframalpha.com/input/?i=x^ {2}%2B%281%2Bx^{2}%29\sin+\theta+where+x+%3D+%281%2Bsin+\theta%29%2Fcos+\theta and I don't see how you get a single number out of that. in other words, I don't really understand how they get a constant number independent of theta... that appears bogus...

8. phi

the link did not post properly