Problems 2 on Trigonometric Definitions: UNIZOR.COM - Math4Teens - Trigonometry - Trigonometric Definitions

Notes to a video lecture on http://www.unizor.com

Trigonometry - More Problems on Definitions

1. Prove that for any angle φ the following equality is true
2·(sin⁶φ + cos⁶φ) + 1 =
= 3·(sin⁴φ + cos⁴φ)

2. Prove that for any angle φ the following equality is true
sin⁸φ − cos⁸φ =
= 4·sin⁶φ−6·sin⁴φ+4·sin²φ-1

3. Calculate a sum of squares of sines of all angles between 0° and 360° whose measure is a multiple of 30°.

4. Given a point A on a unit circle with positive abscissa x_A and positive ordinate y_A. Consider a point B with an abscissa equal to an ordinate of A and an ordinate equal to an abscissa of A.
Prove that a sum of angles represented by points A and B is π/2.

5. Solve an equation sin(x)=cos(x).

6. Solve an equation tan(x)=cot(x).