cot a = tan A; cosec A + cot a = cot a.

If A + B + c = 90°;

Tan A tan B + tan A tan c + tan в tan c = 1;

Cot Acot B + cot c = cot A cot B cot C;

Sin 2 A+ sin 2 B + sin 2 c = 4 cos A Cos B cos C.
If A + B + c = 180°;

Sin A + sin B + sin c = 4 cosa cos B COS C;

Cos A+COS B + cos c =

Tan Atan B + tan c =
Cot A cot B + cot A cot

1 + 4 sina sin B sinc;

tan A tan в tan C; +cot B cot c = 1.

2 sin a = ± √ 1 + sin 2 ▲ ±√1 sin 2 A.

Numerical Values of Functions of some Angles.

Sin 0° 0 = cos 90°; cos 0° = 1 = sin 90°; tan 0° 0 = cot 90°; tan 90° = ∞

= cot 0°;

√3 = cot 75°; tan 60° = √3 = cot 30°;

= cot 60°; tan 75° = 2 + √3 = cot 15°;

√ b2 + c2−2bc cos a = b cos c± √ c2—b2 sin3 C.

If s = area of triangle; s= √s (s-a) (s—b) (s—c) =

S

Radius of escribed circle touching the side a = s-a
Area of quadrilateral inscribed in circle =

√ (s—a) s- -b) (s—c) (s—d) ; s =

a + b + c + d

2

Area of polygon of n sides inscribed in circle whose radius

FORMULE IN SPHERICAL TRIGONOMETRY.

The sides and angles of the polar triangle are the supplements respectively of the angles and sides of the primitive triangle.

A+B+C > π < 3 π.

In any spherical triangle;

Cos a = cos b cos c + sin b sin c cos A.

Sin A sin B sin c :: sin a: sin b: sin c.

:

Cot a sin b = cot a sin c + cos b cos C; cos A =

Area of spherical triangle A+B+C-T

spherical excess

4 right angles

=

2π

× area of hemisphere.

2' sin (A+B)

p being the r drawn from A to side c; s=(a+b+c).

h being the r distance between the parallel sides a, Area of trapezium inscribed in circle =

b.

✅ {(s—a) (s—b) (s—c) (s—d)}, s = {} (a+b+c+d).

na2
4

Area of regular polygon = x cot

180°

η

;

n = number of sides each equal to a.

Area of regular polygon of n sides inscribed in circle,

Circumference of circle = 2πr ; π = 3·14159265 etc. =

ΠΡΑ

Length of arc subtending ▲ A° at centre = 180°

Area of circle = r2; area of sector = πr2 x

A°

360°

p being the perpendicular drawn from the end of the arc a to radius through its origin.

Area of ring between two concentric circles = π (r ̧2—r22) (r1+r2) (r1-r2).

Τι

=

and 72 being the radii of the outer and inner circles.

Surface of solid bounded by rectilineal figures = sum of areas of bounding surfaces.

Curve surface of cylinder = 2xrh; r = rad. of base, h = height;

Whole surface of cylinder 2πr (h+r).