Question

6. Make sure you set up your algebraic equation and solve. Show work!! If those ratios are equal, then what type of angles are they? Draw a diagram. Given: sin(18m - 12) = cos(7m + 2), find the value of m.

Answer 1

m = 4

Step-by-step explanation

If the sine of an angle is the cosine of another angle, this means that the angles are complementary. We can see this in a right triangle:

Since the sum of the interior angles of a triangle is 180º and one of the angles in a right triangle is always 90º, then the sum of the other two angles is 90º:

`\beta=90-\alpha`

The sine of angle alpha is:

`\sin \alpha=(b)/(h)`

The cosine of angle beta is:

`\cos \beta=(b)/(h)`

We can rewrite this as:

`\cos (90-\alpha)=(b)/(h)=\sin \alpha`

Therefore, for this problem, the angles are complementary angles:

`(18m-12)=90-(7m+2)`

Solving for m:

`\begin{gathered} 18m-12=90-7m-2 \\ 18m+7m=90-2+12 \\ 25m=100 \\ m=(100)/(25) \\ m=4 \end{gathered}`