Mathematics: If cosx = tanx, determine all possible values of sinx.in not sure how to do this question. i just wrote sinx = cos^2x but i think there is more to this problem. any ideas tnx a million

The transformation you are referring to is a rotation...

If cosx = tanx, determine all possible values of

Ответ:

manuel6885

13.03.2022

If $\cos x=\tan x$ , then

$\cos x=\dfrac{\sin x}{\cos x}\implies\cos^2x=\sin x$

for $\cos x\neq0$ . This is definitely the case, since $\tan x$ is undefined if $\cos x=0$ . Now, $\cos^2x=1-\sin^2x$ , so we have

$1-\sin^2x=\sin x\implies\sin^2x+\sin x-1=0\implies\sin x=\dfrac{-1\pm\sqrt5}2$

or $x\approx-1.618$ and $x\approx0.618$ . One of these solutions is larger than 1 in absolute value, but $|\sin x|\le1$ , so we omit that solution, leaving us with

$\sin x=\dfrac{\sqrt5-1}2\implies x=\arcsin\left(\dfrac{\sqrt5-1}2\right)+2n\pi$

for integers

, which follows from the fact that $\sin x$ has period $2\pi$ .

0,0(0 оценок)

If cosx = tanx, determine all possible values of sinx.in not sure how to do this question. i just wrote sinx = cos^2x but i think there is more to this problem. any ideas tnx a million

Ответ:

Ответ:

Ask your question to the AI advisor

More tips

Answers on questions: Mathematics

Ask an AI advisor a question