Question

For what value of x is sin x = cos 19°, where 0°< x < 90°?

Answer 1

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The value of x if sin x = cos 19°, where  must be 0°< x < 90°  is  x = 71°.
    
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Answer 2

Answer:  The required value of x is 71°.

Step-by-step explanation:  We are given to find he value of x for which

$\sin x=\cos 19^\circ,$  0°< x < 90°.

We know that

the sine of any acute angle is equal to the cosine of its complement.

So, from the given equation, we can say that

the acute angles with measure x and 19° are complement of each other.

Therefore, we get

$x+19^\circ=90^\circ\\\\\Rightarrow x=90^\circ-19^\circ\\\\\Rightarrow x=71^\circ.$

Thus, the required value of x is 71°.