Trig Definitions - Problems 2: UNIZOR.COM - Math 4 Teens - Trigonometry - Trigonometric Definitions
Channel: Zor Shekhtman on UNIZOR Education
Date: 2022-10-19

UNIZOR.COM - Creative Minds through Art of Mathematics

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·[sin^6(φ) + cos^6(φ)] + 1 = 3·[sin^4(φ) + cos^4(φ)]

2. Prove that for any angle φ the following equality is true
sin^8(φ) − cos^8(φ) = 4·sin^6(φ)−6·sin^4(φ)+4·sin^2(φ)-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 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).