# Angle Thinking

## An Advanced Mathematics Lesson Starter Of The Day

I'm thinking of an acute angle measured in degrees. The tangent of the angle is bigger than the cosine of the angle which in turn is bigger than the sine of the angle.

Without calculator guess what angle I might be thinking of.

With a calculator find a more precise answer to the question above.

Topics: Starter

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Szilvia Varro-Gyapay, Montreal

Friday, September 4, 2020

"Thank you for the great question! I solved the question using partly algebra first:
Because x is an acute angle and sin x < cos x, 0 cos x from which we get (sin x)^2 + sin x - 1 > 0, from which we get that sin x has to be greater than (-1 + sqrt(5))/2, and so on.
I took a look at the solution only after that. So maybe you could add the algebraic way as a second way to solve the question, too."

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