Question

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

Answer 1

`x\approx0.6427876097`

Step-by-step explanation:

Solve for x:

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

Rewrite the right hand side using the following identity:

`sin(\theta)=cos(\theta - (\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`

Answer 2

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 becomecos (90-40) = sin (40)
Cos (50) = sin (40)
Hope this helps