I need help with solving this problem.

Find the value of $\sin2x$, if $\cot x = -\frac{7}{24}$, and $x$ is obtuse.

My attempt to this problem, was as follows :

First I knew that $\cot x$ equals a negative value, so the terminal arm must lie in the $2$-nd or $4$-th quadrant. I made the terminal arm be in the second quadrant, which will make $x$ be an obtuse angle. Then I found my hypotenuse, which is $25$, then I wrote the trigonometric ratios for cosine and sine. Which were : $\cos x = -\frac{7}{25}$ , $\sin x = \frac{24}{25}$. I then used the double angle formula for sine, to substitute my ratios in it, and solve. $$\sin 2x = 2\sin x \cos x$$, and I got $$\sin 2x = -2 \cdot \frac{24}{25} \cdot \frac{7}{25} = -\frac{366}{625}$$

Did I solve this problem correctly ?

  • $\begingroup$ As $$\sin2x=\cdots=\dfrac{2\cot x}{1+\cot^2x}$$ What is the use of "obtuse"? $\endgroup$ – lab bhattacharjee Jan 10 '16 at 14:33
  • $\begingroup$ @labbhattacharjee This is what it said in the question. $\endgroup$ – Viktor Raspberry Jan 10 '16 at 14:40

Yes, your answer is correct. It's nice that the problem made use of the $7, 24, 25$ Pythagorean triple.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.