4 4 θ X θ P θ 4. 0, 405 P 0 X 405 X P 4. () 60 () 45 () 40 (4) 765 (5) 40 B 60 0 P = 90, = ( ) = X

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1 A P P P X X X X X 60 X 0 P P

2 4 4 θ X θ P θ 4. 0, 405 P 0 X 405 X P 4. () 60 () 45 () 40 (4) 765 (5) 40 B 60 0 P = 90, = ( ) = X

3 4.. 5 n P X α P α + 60 n C 0 0 ( ) 60 a a a a 4. ( ) 80 () () 60

4 6 4 (0 80 ) (0 ) (50 ) 5 6 (90 ) (60 ) 6 (0 ) (5 ) 4 (90 ) 4 (45 ) (80 ) 0 (0 ) (80 ) 0 (0 ) () 0 () 5 () (4) 70 (5) 0

5 4.. 7 D r θ( ) l S l = rθ, S = r θ S = lr θ θ r l = rθ θ S rθ r S = r θ = r θ = lr S S = 0 6 = () 4 7 () 6 6

6 sin θ cos θ tan θ θ θ A x θ P(x, ) r r P (x, ) r x r x r r θ θ r x r x sin θ = r, cos θ = x r, tan θ = x r θ θ θ P θ tan θ 4. 4 r r = P (, ) x = = sin 4 = r = = cos 4 = x r = = tan 4 = x = = r Q P Q P r r 4 r x

7 θ sin θ cos θ tan θ () θ = 5 4 () θ = 6 () θ = sin θ cos θ tan θ θ sin θ cos θ tan θ x + x + x 4 4 4

8 θ () sin θ < 0 cos θ > 0 () cos θ < 0 tan θ > 0 B θ P(a, b) sin θ cos θ P(a, b) sin θ = b = b, cos θ = a = a θ cos θ x sin θ sin θ P cos θ P x = sin θ = cos θ α = sin θ α 5 θ α = cos θ α 5 θ θ θ = sin θ = cos θ

9 4.. 4 sin(θ + ) = sin θ, cos(θ + ) = cos θ sin θ cos θ = sin θ = cos θ = sin θ = cos θ θ P(a, b) x = T(, m) tan θ T(, m) P b tan θ = b a = m = m θ a tan θ T = tan θ x α α 5 θ tan θ θ = = tan θ θ θ =

10 4 4 = tan θ θ =, θ = tan(θ + ) = tan θ tan θ = sin θ = cos θ = tan θ C 4.4 = sin ( θ ı ) = sin θ θ = sin ( ) θ ı θ = sin θ 40 θ = cos θ = sin ( θ + ) = cos θ = sin θ θ

11 4.8 () = cos ( ) θ () = sin ( θ + 6 ) () = tan ( θ 4 )

12 = sin θ = sin θ θ = sin θ 5 7 θ = sin θ 4.9 () = cos θ () = sin θ

13 4.6 = sin θ θ = α sin θ θ = α sin θ = sin θ α θ α θ = sin θ = sin θ 5 7 θ 4.6 sin θ sin θ k sin kθ cos kθ k tan kθ k sin(kθ+)=sin kθ sin k(θ+ k )=sin kθ 4.0 () = cos θ

14 46 4 () = sin θ () = tan θ f(x) 0 p f(x + p) = f(x) f(x) p f(x + p) = f((x + p) + p) = f(x + p) = f(x) p p p

15 sin(θ + ) = sin θ tan(θ + ) = tan θ A tan θ = sin θ cos θ + tan θ = cos θ sin θ + cos θ = 4. θ cos θ = 5 sin θ tan θ sin θ = cos θ = ( ) = θ sin θ < 0 6 sin θ = 5 = 4 5 tan θ = sin θ ( cos θ = 4 ) ( ) 5 5 ( = 4 ) ( 5 ) = θ 5 x 4. θ 4 sin θ = cos θ tan θ

16 θ 4 tan θ = sin θ cos θ cos θ = + tan θ = + ( ) = 5 θ 4 cos θ > 0 cos θ = 5 = 5 θ x sin θ = tan θ cos θ = ( ) 5 = 5 4. θ tan θ = sin θ cos θ B 4. tan θ + tan θ = sin θ cos θ = sin θ cos θ + cos θ sin θ = sin θ sin θ cos θ + = sin θ + cos θ sin θ cos θ cos θ sin θ cos θ = sin θ cos θ tan θ + tan θ = sin θ cos θ tan θ = cos θ sin θ sin θ+cos θ=

17 () (sin θ + cos θ) + (sin θ cos θ) = () tan θ sin θ = tan θ sin θ 4. sin θ + cos θ = () sin θ cos θ () sin θ + cos θ () sin θ cos θ (sin θ + cos θ) () a + b = (a + b)(a ab + b ) () sin θ + cos θ = sin θ + sin θ cos θ + cos θ = 4 sin θ+cos θ= + sin θ cos θ = 4 sin θ cos θ = 8 () sin θ + cos θ=(sin θ + cos θ)(sin θ sin θ cos θ + cos θ) =(sin θ + cos θ)( sin θ cos θ) = { ( )} 8 = 8 = 6

18 sin θ + cos θ = () sin θ cos θ () sin θ + cos θ 4.5 sin θ cos θ = () sin θ cos θ () sin θ cos θ

19 4.. 5 C sin(θ + n) = sin θ cos(θ + n) = cos θ n tan(θ+n)=tan θ tan(θ + n) = tan θ 4.7 () sin = sin 7 = sin () tan 7 = tan 4 = tan = = + = f(x) f( x) = f(x) f( x) = f(x) f(a) = f(x) a a x f(a) = f(x) f(a) a a x sin( θ) = sin θ =sin θ cos( θ) = cos θ =cos θ tan( θ) = tan θ =tan θ ( 4.8 () sin ) = sin = ( () cos ) = cos ( ) = cos + 4 = cos =

20 ( () sin ) () cos ( 6 ) 6 () tan ( 94 ) ( sin θ + ) = cos θ ( 4 cos θ + ) = sin θ ( tan θ + ) = tan θ sin(θ + ) = sin θ cos(θ + ) = cos θ tan(θ + ) = tan θ θ + P(a, b) θ x R( b, a) θ+ θ P(a, b) x Q( a, b) a = cos θ b = sin θ a = cos θ b = sin θ sin(θ + ) = b = sin θ sin ( θ + ) = a = cos θ cos(θ + ) = a = cos θ cos ( θ + ) = b = sin θ

21 A θ < sin θ + = 0 sin θ = θ P Q θ 0 θ < P Q x θ = 7 6, 6 P 6 Q 4.4 θ 5 θ = n, θ = + n (n 6 ) θ < () sin θ = () cos θ + = 0 () sin θ + = 0

22 tan θ = θ x = 0 θ < x = θ = θ x θ = + n (n ) 4.8 () tan θ = () tan θ =

23 θ < 5 sin θ cos θ + 4 = 0 cos θ = sin θ sin θ sin θ 5 sin θ ( sin θ) + 4 = 0 sin θ + 5 sin θ + = 0 ( sin θ + )(sin θ + ) = 0 sin θ sin θ + = 0 sin θ+>0 0 θ < sin θ = θ = 7 6, θ < () cos θ + 5 sin θ 4 = 0 () sin θ + cos θ = 0

24 56 4 B θ < cos θ 0 θ < cos θ = θ θ = 4, 7 4 x θ = = cos θ = 4 = cos θ 0 θ < cos θ > 7 4 θ 0 θ < 4, 7 4 < θ < θ < () sin θ > () cos θ

25 () tan θ < 4..5 () (sin θ + cos θ) + ( sin θ cos θ) = () cos(θ + ) + cos( θ) = () sin θ = () cos θ =

26 58 4 = sin θ + sin θ = sin θ + sin θ () sin θ = x = a(x p) + q () θ () 5 () 0 () θ = 4 + n θ = 5 + n (n ) () θ = 4 + n θ = 5 + n (n 4 ) () = (x + ) ()

27 α β sin(α + β) cos(α + β) α β tan(α + β) A P sin(α+β) sin(α + β) = HK = HQ + QK HQ = PQ cos β = sin α cos β QK = Q sin β = cos α sin β P H β Q α β S K x sin(α + β) = sin α cos β + cos α sin β P x cos(α + β) cos(α + β) = S = K PH K = Q cos β = cos α cos β, PH = PQ sin β = sin α sin β cos(α + β) = cos α cos β sin α sin β α β 4. β β sin(α β) = sin α cos β cos α sin β cos(α β) = cos α cos β + sin α sin β

28 60 4 sin(α + β) = sin α cos β + cos α sin β sin(α β) = sin α cos β cos α sin β cos(α + β) = cos α cos β sin α sin β 4 cos(α β) = cos α cos β + sin α sin β () sin 75 =sin( ) =sin 45 cos 0 + cos 45 sin 0 = + = + = ( + ) = () sin 5 =sin(45 0 ) =sin 45 cos 0 cos 45 sin 0 = 6 = = 4 4. () cos 75 () cos 5

29 4.. 6 B 5 tan(α + β) = 6 tan(α β) = tan(α + β) = tan(α + β) = sin(α + β) cos(α + β) tan α + tan β tan α tan β tan α tan β + tan α tan β sin α cos β + cos α sin β cos α cos β sin α sin β cos α cos β tan(α + β) = sin α cos α + sin β cos β sin α cos α sin β cos β = tan α + tan β tan α tan β β β 6 tan 75 = tan( ) = tan 45 + tan 0 tan 45 tan 0 = + = + = ( + ) ( )( + ) = + + ( = 4 + ) = + 4. () tan 05 () tan 5

30 tan α = tan β = tan(α β) α β 0 < α β < 90 tan(α β) = tan α tan β + tan α tan β = + ( ) = 0 < α β < 90 tan(α β) = α β α β = tan α = tan β = tan(α + β) α + β 0 < α + β < 80 x = mx θ tan θ = m tan θ = m = x = x x α β tan α = tan β = θ θ = α β α β = x θ = mx θ α β x = x x

31 sin(α + β) = sin α cos β + cos α sin β cos(α + β) = cos α cos β sin α sin β sin α cos α sin α sin α A β = α sin α = sin α cos α cos α = cos α sin α cos α = sin α cos α = cos α cos α= sin α sin α= cos α sin α 4.8 = tan α + cos α sin α cos α = + ( cos α ) sin α + cos α = sin α cos α cos α = sin α cos α = tan α = tan α 4.5 () (sin α + cos α) = + sin α

32 64 4 () cos 4 α sin 4 α = cos α cos α = sin α cos α = α cos α α sin α = cos α, cos α = + cos α 4. cos 8 ( cos 8 = ( + cos ) = ) + = cos 8 > 0 cos 8 = + + = sin 8

33 tan α = tan α tan α, α tan = cos α + cos α 4.7 () tan α = tan α () 0 < α < cos α = tan α

34 θ < cos θ + cos θ + = 0 cos θ ( cos θ ) + cos θ + = 0 cos θ( cos θ + ) = 0 cos θ = 0 cos θ = 0 θ < cos θ = 0 θ =, cos θ = θ = 4 ( ) θ = θ < () cos θ + sin θ = () sin θ + cos θ = 0

35 B a sin θ + b cos θ sin θ + ( cos θ = sin θ + ) ( = sin θ cos + cos θ sin ) ( ) = sin θ + cos θ = sin θ + cos θ = a sin θ + b cos θ r sin(θ + α) (a, b) P x P α P = r b P(a, b) r r cos α = a, r sin α = b α a x a sin θ + b cos θ = r cos α sin θ + r sin α cos θ = r(sin θ cos α + cos θ sin α) = r sin(θ + α) r = a + b a sin θ + b cos θ a sin θ + b cos θ = a + b sin(θ + α) cos α = a a + b, sin α = b a + b

36 () sin θ + cos θ = ( sin θ + ) 4 ( () sin θ cos θ = sin θ ) 6 () () 4 P(, ) x 6 P(, ) x 4.9 r sin(θ + α) < α < () sin θ + cos θ () sin θ cos θ 4.9 = sin x + cos x sin x + cos x = ( sin x + ) 4 = ( sin x + ) 4 ( sin x + ) 4 4.()

37 = ( sin x + ) 4 = ( sin x + ) = sin x x = sin x x = sin x + cos x

38 x < sin x cos x = r sin(x + α) x + α sin(x + α) x + α ( sin x ) = 6 ( sin x ) = 6 0 x < 6 x 6 < 6 x 6 = 6 x 6 = 5 6 x =, x < = sin x cos x = x x

39 x < sin x + cos x = () sin α = sin α 4 sin α () cos α = cos α + 4 cos α

40 θ < () sin θ sin θ () cos θ < sin θ + 6 = sin x cos x

41 = sin x + cos x 4 α = α + α 5 () 0 θ, θ 5 () 0 < θ <, 7 6 < θ < x 7 5 5

42 A () sin 6 () cos 7 ( () tan ) 6 () = cos θ ( () = sin θ + )

43 () tan θ sin θ sin θ tan θ = sin θ tan θ () cos θ tan θ = tan θ sin θ 4 0 x < () cos x sin x = 0 () cos x = cos x

44 ( ) () sin θ = cos θ () cos( θ) = cos θ 6 α β 4 sin α = 5 cos β = 4 5 () cos α () sin β () sin(α + β) (4) sin(α β) (5) cos(α + β) (6) cos(α β)

45 = sin x cos x (0 x < ) () () = 0 x () 0 x 4.. B 8 0 θ < = cos θ + sin θ θ

46 () sin α + sin β = cos α + cos β = cos(α β) () tan α = tan β = 4 tan γ = tan(α + β + γ) 0 sin(α β) sin(α + β) = tan α tan β tan α + tan β

47 () = sin x () = cos x () sin x + sin x = sin x cos x () 0 x < sin x + sin x = 0

48 80 4 = sin x cos x sin x + (0 x ) 9 () cos α cos β sin α sin β tan{(α + β) + γ} () () sin x = sin(x + x) a sin θ + b cos θ () () 0 ()

49 4.. 8 () θ () θ [ () = cos θ cos θ () = cos θ sin θ sin θ cos θ 4 () x = 6, 5 6, () x = 0,, 4 ( ) 5 () sin θ =sin cos θ cos sin θ = cos θ 0 sin θ = cos θ () cos( θ)=cos cos θ + sin sin θ = cos θ + 0 sin θ = cos θ 6 () 4 5 () 5 () 4 5 (4) 0 (5) () () x =, 4 () 0 x, 4 x < [ = sin (6) ( x ) ] ] 8 θ = sin θ = x x = (x ) + 9 () 59 7 () [ () tan(α + β) = 6 7 ] + β) + tan γ tan(α tan(α + β) tan γ

50 8 4 0 sin(α β) sin(α + β) = sin α cos β cos α sin β sin α cos β + cos α sin β cos α cos β sin(α β) sin(α + β) = sin α cos α sin β cos β sin α cos α + sin β cos β = tan α tan β tan α + tan β () x [ () = + cos x ] x () sin x = sin(x + x) = sin x cos x + cos x sin x sin x = sin(x x) = sin x cos x cos x sin x () x = 0,,, () () sin x = 0 cos x = 0 x = 8 x = 5 [ 8 = (x sin + ) ] 4

1 (1) ( i ) 60 (ii) 75 (iii) 315 (2) π ( i ) (ii) π (iii) 7 12 π ( (3) r, AOB = θ 0 < θ < π ) OAB A 2 OB P ( AB ) < ( AP ) (4) 0 < θ < π 2 sin θ

1 (1) ( i ) 60 (ii) 75 (iii) 315 (2) π ( i ) (ii) π (iii) 7 12 π ( (3) r, AOB = θ 0 < θ < π ) OAB A 2 OB P ( AB ) < ( AP ) (4) 0 < θ < π 2 sin θ 1 (1) ( i ) 60 (ii) 75 (iii) 15 () ( i ) (ii) 4 (iii) 7 1 ( () r, AOB = θ 0 < θ < ) OAB A OB P ( AB ) < ( AP ) (4) 0 < θ < sin θ < θ < tan θ 0 x, 0 y (1) sin x = sin y (x, y) () cos x cos y (x, y) 1 c

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