To solve the equation sin x = cos 19, we can use the identity that relates sine and cosine:
sin x = cos (90 – x). This means we can set up the equation:
cos (90 – x) = cos 19
From the properties of cosine, we know that if cos A = cos B, then:
- A = B + 360n or
- A = -B + 360n (where n is any integer)
In our case, since we’re dealing with degrees and x must be between 0 and 90 degrees, we only need to consider the first option.
So:
90 – x = 19
Solving for x gives:
x = 90 – 19
x = 71
Therefore, the value of x that satisfies the equation sin x = cos 19 for 0 < x < 90 is x = 71 degrees.