Question

What is the value of x?

sin 55° = cos x

Answer 1

Cos x= 35 degrees.
90-55=35

Answer 2

Answer:  The required value of x is 35°.

Step-by-step explanation:  We are given to find the value of x from the following trigonometric equation:

$\sin 55^\circ=\cos x~~~~~~~~~~~~~~~~~~~~~~~~(i)$

We know that the sine of any acute angle is equal to the cosine of its complement and cosine of any acute angle is equal to the sine of its complement.

So, from equation (i), we get

$\sin 55^\circ=\cos x\\\\\Rightarrow \sin 55^\circ=\sin(90^\circ-x)\\\\\Rightarrow 55^\circ=90^\circ-x\\\\\Rightarrow x=90^\circ-55^\circ\\\\\Rightarrow x=35^\circ.$

Thus, the required value of x is 35°.