Name: Elle
Who is asking: Student
Level of the question: Secondary

Question: Hi. I have a question as follows:
Solve the equation cos x = sin 20 where x is acute.

as complimentary angles add up to 90 degrees, i did 90-20=70, so
cos 70 = sin 20.
Is this all i have to do to correctly solve the equation or is there are more formal way of showing how i worked it out?
Your help would be much appreciated,


Good work, Elle. That is quite correct and your reasoning is just fine. One thing to be aware of: this will work if both angles are acute, but not necessarily in other situations.

If you want another way to look at it, consider a right triangle where one angle is 20 degrees. The sine of that angle is the opposite side over the hypotenuse. The cosine of the other angle is its adjacent side (which is the same as the sine's opposite side) over the hypotenuse. So the sine of one angle is the cosine of the other. Since you know that in any triangle, the angles add up to 180, the missing angle is 180 - 90 - 20 = 70 degrees.

Stephen La Rocque>