This exercise shows how to obtain radical expressions for
Chapter 6, Problem 52(choose chapter or problem)
This exercise shows how to obtain radical expressions for sin 15 and cos 15. In the figure, assume that AB BD 2.(a) In the right triangle BCD, note that DC 1because is opposite the 30 angle and BD 2.Use the Pythagorean theorem to show thatBC (b) Use the Pythagorean theorem to show thatAD (c) Show that the expression for AD in part (b) is equalto Hint: Two nonnegative quantities areequal if and only if their squares are equal.(d) Explain why BAD BDA.(e) According to a theorem from geometry, an exteriorangle of a triangle is equal to the sum of the twononadjacent interior angles. Apply this to ^ABDwith exterior angle DBC 30, and show thatBAD 15.(f) Using the figure and the values that you have obtainedfor the lengths, conclude that(g) Rationalize the denominators in part (f) to obtain(h) Use your calculator to check the results in part (g).sin
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