Question

What is the value of x?

sin 55° = cos x

Answer 1

The value of x is 35°.

The sine and cosine functions are complementary functions, which means that sin(90° - x) = cos(x) and cos(90° - x) = sin(x).

The sine and cosine functions are even functions, which means that sin(-x) = -sin(x) and cos(-x) = cos(x).

The sum of the squares of the sine and cosine functions is equal to 1, which means that sin²(x) + cos²(x) = 1.

Using these properties, we can solve for the value of x in the equation sin(55°) = cos(x).

Since sin(55°) = cos(35°),

we know that x must be equal to 35°.

This is because sin(55°) and cos(35°) are complementary functions, which means that they are equal to each other.

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°.