Question

Solve the equation cos x° = sin 40°, where 0 < x < 90.

Answer 1

For 0 < x < 90

cos (90-x) = sin (x), 

and sin (90-x) = cos(x)

Let's just try and pick the top one, the equation will become

cos (90-40) = sin (40)

Cos (50) = sin (40)

Hope this helps

Answer 2

Answer:

$x\approx0.6427876097$

Explanation:

Solve for x:

$cos(x)=sin(40)\\\\0<x<90$

Rewrite the right hand side using the following identity:

$sin(\theta)=cos(\theta - \frac{\pi}{2} )=cos( \theta- 90)$

Therefore:

$cos(x)=cos(40-90)=cos(-50)$

Since cosine function is an even function:

$cos(-\theta) =cos(\theta)$

Hence:

$cos(-50)=cos(50)$

$cos(x)=cos(50)$

Finally, take the inverse cosine of both sides:

$x\approx0.6427876097$