(4) (b) m. (c) (d) sin α cos α = sin 2 k = sin k sin k. cos 2 m = cos m cos m. (g) (e)(f) sin 2 x + cos 2 x = 1. (h) (f) (i)

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Download "(4) (b) m. (c) (d) sin α cos α = sin 2 k = sin k sin k. cos 2 m = cos m cos m. (g) (e)(f) sin 2 x + cos 2 x = 1. (h) (f) (i)"

Lidia Dobrowolska
5 lat temu
Przeglądów:

1 (3) (e) sin( θ) sin θ cos( θ) cos θ sin(θ + π/) cos θ cos(θ + π/) sin θ sin(θ π/) cos θ cos(θ π/) sin θ sin(θ ± π) sin θ cos(θ ± π) cos θ sin(θ ± π) sin θ cos(θ ± π) cos θ (f) cos x cos y (g) sin x sin y (h) sin x cos y (i) m cos(mπ) ( 1) m sin(mπ) cos(x + y) + cos(x y) cos(x + y) + cos(x y) sin(x + y) + sin(x y) (4) sin(π/ θ) sin(θ π/) cos θ m sin(θ ± mπ) sin θ cos(θ ± mπ) cos θ sin(θ + 3π/) sin(θ + π π/) sin α cos α (e) (f) sin(θ π/) cos θ sin(α + α) + sin(α α) sin(α) sin α cos α sin k sin k sin k cos(k + k) + cos(k k) cos m cos m cos m (g) (e)(f) sin x + cos x 1 (h) (f) cos(m + m) + cos(m m) sin α cos(k) + 1 cos(m) + 1 cos(x) cos x 1 cos x (1 cos x) cos x sin x (i) sin θ + b cos θ + b sin(θ + α) α tn 1 b 1

2 (3) [ ] sin( θ)? cos( θ)? sin(θ + π/)? cos(θ + π/)? sin(θ π/)? cos(θ π/)? sin(θ ± π)? cos(θ ± π)? (e) sin(θ ± π)? cos(θ ± π)? (f) cos x cos y? (g) sin x sin y? (h) sin x cos y? (i) m cos(mπ)? sin(mπ)? (4) [ ] sin(π/ θ)?? m sin(θ ± mπ)? cos(θ ± mπ)? sin(θ + 3π/)??? sin α cos α?? sin(α)? (e) sin k??? (f) cos m??? (g) (e)(f) sin x + cos x? (h) (f) cos(x)??? (i) sin θ + b cos θ? α?

3 (6) e e ln, b, c, (!!) (8) ( ) e e b e +b (c e ) ( e b ) (c) e +b (e ) b e b ( e) b b e b (e) b e + e b sin θ cos θ θ cos θ sin θ θ x ex e x (f) b c e + e b c e + e (c + ) e (7) e e e 4 e 6 {e 3 e } 3 {e 5 } 3 e 15 {9 e } {(1/3) e } 3 e 3 3 e e e (e) e 5 + e (f) e π + e π (9) {x sin x} x x x sin x + x x sin x sin x + x cos x {sin θ cos θ} θ θ sin θ cos θ + sin θ θ cos θ cos θ sin θ cos θ 1 cos θ (g) () e jπ + e jπ cos π y {sin y} y sin y sin y + sin y y sin y sin y cos y z {cos (z)} z cos(z) cos(z) + cos(z) z cos(z) 4 sin(z) cos(z) 3

4 (6) [ ] e e ln, b, c, (!!) (8) [ ] ( ) e e b? (c e ) ( e b )? (e ) b? ( e) b? (e) b e + e b? sin θ? θ cos θ? θ x ex? (f) b c e + e b?? (9) [ ] (7) [ ] e e e 4? {e 3 e } 3?? {9 e } {(1/3) e }?? 3 e e? (e) e 5 + e? (f) e π + e π? (g) () e jπ + e jπ?? {x sin x}? x? {sin θ cos θ}? θ y {sin y}????? z {cos (z)}?? 4

5 (1) (1) sin θ θ [ cos θ] b cos b + cos cos θ θ [sin θ] b sin b sin e x x [e x ] b e b e (/x) ( / x) {bcef x} bcef x y {αβxz} (11) x sin x x x e x x x ( cos x) x x [ x cos x] b + cos xx b cos b + cos + sin b sin x x ex x [x e x ] b e x x b e b e e b + e {θ cos x sin y} cos x sin y θ θ cos( α + β θ + γ) sin( α + β θ + γ) α + β (e) x y {x y} [ ] x y {x y} { x } x x [ sin y cos y y ] b sin b sin sin x x ( ) 1 cos x x 1 x cos x [ ] b sin x x (3)-(e) 1 [x]b 1 b sin b sin 4 5

6 (1) [ ] (1) [ ] sin θ θ?? cos θ θ?? e x x?? (/x) ( / x) {bcef x}? x {αβxz}? y (11) [ ] x sin x x??? {θ cos x sin y}? θ θ cos( α + β θ + γ)? x e x x??? cos y y?? (e) x y {x y}??? sin x x???? (3)-(e) 6

7 (13) c ef x c ef[x] b c ef(b ) T w( ) m T/ T/ [ ] T/ sin(t) cos(t) t 1 { sin T sin T 1 { sin T + sin T T sin w π/t sin mπ T/ (3)-(i) (ii) m } } T w( ) m T/ w π/t [ sin(t) cos(t) t 1 T sin 1 sin mπ ] T/ (3)-(i) (ii) m T/ cos() t (14) T/ t T n i1 x i x 1 + x + + x n T/ cos() t T/ T/ T/ t T i n T w( ) m T/ T/ [ ] T/ cos(t) sin(t) t 1 { cos T + cos T 1 T/ { cos T + cos T (ii) m T/ T/ sin() t } } i1 i1 { x i } 1 n i1 i1 (e) {x i y j } x i x i j1 j1 y j j (f) x i ( n ) x i x i i1 i1 7

8 (13) [ ] c ef x?? T w( ) m T/ T/ cos(t) t???? w π/t?? (3)-(i) (ii) m T/ T/ cos() t?? T w( ) m T/ T/ sin(t) t???? (ii) m T/ T/ sin() t? T w( ) m T/ cos(t) t?? w π/t?? (3)-(i) (ii) m T/ cos() t?? (14) [ ] i1 n i1 i1 x i? 1???? n i1 { x i }? (e) n j1 {x i y j }? j (f) x i x i? i1 8

9 (g) k α k α n, (n k) (h) n i1 j1 {α n x n } α k x k m x ij (x i1 + x i + + x im ) i1 (x 11 + x x 1m ) + (x 1 + x + + x m ) + (x n1 + x n + + x nm ) m i1 j1 n,m i1,j1 (i) m m {x i y j } x i y j i1 j1 { n } m x i y j i1 j1 i1 j1 (15) f(t) f( t) f(t) f( t) f(t) (16) f(t) f(t)t f(t) f(t)t f(t)t + f(t)t + f(t)t + f(t)t + f(t)t f(t)t f(t)t f(t)t f(t)t f(t) b f(t)t f(t) f(t)t f(t) g(t) h(t) f(t) + g(t) (e) f i (t) h(t) i f i(t) (f) f i (t) h(t) i f i(t) (g) f(t) g(t) h(t) f(t) g(t) (h) f(t) g(t) h(t) f(t) g(t) (i) f(t) g(t) h(t) f(t) g(t) 9

10 (g) k α k α n, (n k) (h) n i1 j1 {α n x n }? m x ij?? m i1 j1 n,m i1,j1 (i) i1 j1 m {x i y j }?? (16) [ ] f(t) f(t)t??? f(t) f(t)t??? (15) [ ] f(t)? f(t) b f(t)? f(t)t? f(t)? f(t) g(t) f(t) f(t)t? h(t) f(t) + g(t)? (e) f i (t) h(t) i f i(t)? (f) f i (t) h(t) i f i(t)? (g) f(t) g(t) h(t) f(t) g(t)? (h) f(t) g(t) h(t) f(t) g(t)? (i) f(t) g(t) h(t) f(t) g(t)? 1

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