Εικόνες σελίδας
PDF
Ηλεκτρ. έκδοση

(6.)

Different arcs whose sine, or cosine is the same.

sin (2na ta)

sin (2n+1.7 Fa),

= - sin (2n +1.7+a);
sin (2n + a) = -sin (2n7-a),
sin (2n +1.7-a)= – sin (2n +1.7 +a).
cos (2n7 + a)

cos (217-a),
cos (2n +1.7 - a) = cos (2n +1.7 + a),
cos (2n +a) = -cos (2n +1.7+ a),

cos (+a)= cos (-a),

sin (+a)= – sin (-a).
sin (2n +.a)= cos (2n+ a),
cos (2n+2. Fa)= F sin (2na + a),
sin (2n+a)= -cos (2n7 +a),
cos (2n + + +a)= + sin (2n7. +a).

sin (I+a)= cos a,
cos (fm+a)= + sin a. L. 36-41; C. 6481.)

3

[blocks in formation]

cos a.tan a.

[ocr errors]

COS a

cot a

1.

2.cotla + tan

3. įV3{sin (30° +a)-sin (30°—a)}. 2.sin (45° + 4 a) – 1-2.sin (45o – Ža)) 1-tan (45° -1a) 1+tan (45o – 1a)

a] tan (45° + {a) – tan (45o – ļa) tan (45° + ļa)+ tan (45o – 1a) sin (60° + a)- sin (60° – a).

[merged small][ocr errors][ocr errors]

12

2 tana

1 + (tan La)?

(8.)

Values of cos a. sin a

1- (tana) tan a

1+ (tan ļa)? sin a , cot a.

cot tan

a 1- (sin a)*7*:

cot {a + tan ļa 1 + (tan a)? |

1 cot a.1 + (cot a):)" 1 + tan a.tana

2 (cos ļa)*-- (sin La). 1–2 (sinį a)?

tan (45° + 1 a) + cot (45° +1a) 2 (cos į a) -1. 2 cos (45° + ļa) cos (45° — a). {(1 + cos 2a)]

cos (60° + a) + cos (60° – a).

[merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small]

tan (a + b)= 1 I tan a . tan b

tan a + tan b 1 F a

cot a.cot 671 cot (a+b)=

cot b + cota sin (45° +6) 2

(cos b+sin b). cos (45o = 6)

1+ tan.b tan (45° +6)=

1 Ftan.6

1+ sin b tan (45° +26)=

cos 6 17 sin 6 1+ sin b

[ocr errors]

cos 6

tan (45° +6)= 1 F sin b

tan a

cot a

tan 5

sin a

=

sin (a + b)

tan a + tan b cot b + cot a sin (a-6)

tan b

cot b-cot a cos (a + b) cot b-tan a cos (a - b) cot b + tan a cot a + tan b sin a + sin 6 tan į (a+b)

sin b tanļ (ab) cos b + cos a cot (a+b) cos bcos a tanį (ab) sin a + sin b cos - cos a

=tan { (a + b). cos a + cos b

sin b sin a.cosb= { sin (a + b) + { sin (a - b). cos a.sin b= { sin(a+b)- Įsin (a - b). sin a.sin b={cos(a - b) { cos (a + b). cos a.cos b={cos (a + b)+{cos (a - b). sin a + sin b=2 sin I (a + b).cosį (a - b). cos a +cos b=2 cos } (a +b).cosį (ab). sin a — sin b=2 sinį (ab).cosz (a + b). cos b- cos a=2 sin ? (a - b). sinį (a + b).

sin a

sin (a+b) tan a +tan b=

cos a.cos 6

sin (a+b) cot 6+cot a=

sin a.sin b (sin a) – (sin 6)

sin (a + b). sin (a - b). (cos b) – (cosa) (cos a) – (sin b)

=cos (a + b).cos (a6). (cos b) – (sin a))

sin (a + b). sin (ab) tan a tan be

cos a.cos b

sin (a + b). sin (a - b) cot b-cot ar

sin a.sin b sin b=sin (a + b).cos a cos (a + b). sin cos b=sin (a + b). sin a + cos (a + b).cos a. sin (n + 2) a + sin na=2 sin (n + 1) a.cos a. sin (n + 2)a - sin na=2 cos (n + 1) a.sin a. cos na +cos (n + 2) a=2 cos (n + 1) a.cos a.

cos (n + 2) a=2 sin (n + 1) a.sin a. sin (n +2) a.sin na=sin (n + 1) a) – (sin a)?:

(L. 43—54; W. Ch. ii.)

a.

cos na

;

(11.) Formula relating to double arcs.

2 sin 2a=2 sin a.cos a.

tan 2a=

cot a tan a cos 2a=(cos a) – (sin a)”;

(cot a)? — 1

; = 2 (cosa) - 1;

cot 2a=

2 cot a =1-2 (sin a).

1 (cot a - tan a). 2 tan a

(sec a) tan 2a= 1 – (tan a)

1- (tan a) 2 cot a

1 + (tan a) (cot a) – 1

1-(tan a)?

2

sec 2a=

;

[merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][ocr errors][merged small][ocr errors][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small]

(12.) Values of the sine, cosine, fc. of 30°, 45°, and 60°.

sin 30o = cos 60°

cos 30°=sin 60°={V3, tan 30o =cot 60°= {V3, cot 30°=tan 60°=V3, sec 30°=cosec 60°=V3, cosec 30°=sec 60° = 2. sin 45o = cos 45o = 1 V2, tan 45o = cot 45o = 1, sec 45o = cosec 45o = V2.

« ΠροηγούμενηΣυνέχεια »