chapt 2.3 & 2.4 - circle properties , pythagoras theorem

Question 1

what is a chord ?

Answer 1

a chord ; a line in a circle that does not pass the center – not a diameter

Question 2

circle properties

Answer 2

1) tangent from ext. point
2) tangent perpendicular to radius
3) angles in a semicircle
4) angles at center = 2 x angles at circumference
5) angles in same seg.
6) angles in opposite seg.

Question 3

trigo ratio of acute angles

Answer 3

1) opp/adj = tan
2) adj/hyp = cos
3) opp/hyp = sin

Question 4

trigo ratio of obtuse angles

Answer 4

when θ is obtuse e.g; 90° < θ < 180°

1) sin θ = sin (180° - θ)
2) cos θ = - cos (180° - θ)
3) tan θ = - tan (180° - θ)

Question 5

sine rule

Answer 5

1) side : a/sin A = b/sin B = c/sin C

2) angles: sin A/a = sin B/b = sin C/c

Question 6

cosine rule

Answer 6

side: a² = b² + c² - 2bc Cos A
angles: Cos A = (b² + c² - a²) / 2bc

Question 7

bearings

Answer 7

1) all is measured from the north

2) all angles are must be 3 digits