Question

if sin 41° is equal to K find cos 49° tan 49° and Cos 41° in terms of k

Answer 1

sin 41=cos 49=k
tan 49= sin 49/cos 49=sin 49/k
cos^2 41+ sin^2 41=1
sin 41=k
Therefore cos^2 41=1-k^2
cos 41= square foot of 1-k^2
Hope this helped.

Answer 2

$\cos 41=\sqrt{1-k^2}$

Step-by-step explanation:

We have,

$\sin 41=k$

To find, $\cos 41$ in terms of k = ?

∴ $\cos 49 \tan 49$

=$\cos 49.\dfrac{\sin 49}{\cos 49}$

Using trigonometric identity,

$\tan A=\dfrac{\sin A}{\cos A}$

$=\sin 49.\dfrac{\cos 49}{\cos 49}$

$=\sin 49$

$=\sin (90-41)$

$=\cos 41$

Using trigonometric identity,

$\cos A=\sin (90-A)$

$=\sqrt{1-\sin^2 41}$

Using trigonometric identity,

$\cos A=\sqrt{1-\sin^2 A}$

$=\sqrt{1-k^2}$

Hence, $\cos 41=\sqrt{1-k^2}$