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 =
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 xA and positive ordinate yA. 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).