4. 98 () θ a = 5(cm) θ c = 4(cm) b = (cm) () D 0cm 0 60 D 99 () 0m O O 7 sin 7 = 0.60 cos 7 = 0.799 tan 7 = 0.754 () xkm km R km 00 () θ cos θ = sin θ = () θ sin θ = 4 tan θ = () 0 < x < 90 tan x = 4 sin x = cos x =
4 98 () (sine) (cosine) (tangent) c b c b c b θ a θ a θ a sin θ = b c cos θ = a c tan θ = b a () = D + D D D D D 99 () O () 00 a + b = c ( ) a ( ) + b = c c b b a = c a c ( ) + b ( ) = c a a cos θ + sin θ = tan θ = sin θ cos θ + tan θ = cos θ θ c a b
4 98 () sin θ = 5 cos θ = 4 5 tan θ = 4 () tan 0 = D D D = D tan 0 = 0 = 0 tan 60 = D D D = D tan 60 = 0 = 0 = D + D = 0 + 0 = 40 (cm) 99 () tan 7 = O = O tan 7 = 0 0.754 = 7.54 (m) () O O D O D H O = θ H = r tan θ = O = R (x + R) R = R x + xr OH O OH = O = θ tan θ = OH H = R r r R x + xr = R r r 0 0 60 r R O θ x H R O D 7 0 m D
4 R x + xr = R r r R r = (R r )(x + xr) (x + xr + R )r = R (x + xr) r = R x + xr x + R (km) 00 () sin θ = ( ) sin θ = cos θ = = 8 9 θ sin θ > 0 sin θ = () tan θ = 5 = 5 5 cos θ = sin θ = 6 = 5 6 θ cos θ > 0 cos θ = 5 4 tan θ = sin θ cos θ = θ tan θ > 0 tan θ = cos θ = 6 5 = 5 () 4 5 4 4 θ θ 5 = 5 = tan θ = 5 5 5 5 sin x = 5, cos x = 4 5 cos x = + tan x = + 9 6 = 5 6 cos x = 6 5 0 < x < 90 cos x > 0 cos x = 4 5 x 5 4 sin x cos x = tan x sin x = tan x cos x = 4 4 5 = 5
4. 0 () θ sin θ = 4 5 cos θ = tan θ = () 0 θ 80 cos θ = 5 sin θ tan θ () 0 θ 80 tan θ = sin θ = cos θ = 0 POE = θ (0 θ 80 ) cos θ = x = x, sin θ = y = y, tan θ = y x θ 90 < θ < 80 cos θ < 0, sin θ > 0, tan θ < 0 P x y y θ O E x
4 0 () sin θ = 4 5 ( ) cos θ = sin θ = 4 = 9 5 5 θ cos θ < 0 cos θ = 9 5 = 5 4 tan θ = sin θ cos θ = 5 = 4 5 y θ O 4 5 x () cos θ = 5 ( sin θ = cos θ = ) = 5 5 0 θ 80 sin θ 0 sin θ = 5 = 5 5 y θ O x tan θ = sin θ cos θ = 5 5 = () cos θ = + tan θ = + ( ) = 9 cos θ = 9 0 θ 80 tan θ < 0 θ cos θ < 0 cos θ = 9 = tan θ = sin θ cos θ sin θ = tan θ cos θ = ( ) =
4. 90 80 0 tan (90 θ) = 7 tan θ = 0 (sin 0 cos 0 ) + (sin 70 + cos 70 ) = 04 sin 60 cos 70 + cos 0 sin 70 0 sin (90 θ) = cos θ cos (90 θ) = sin θ tan (90 θ) = sin (90 θ) cos (90 θ) = cos θ sin θ = tan θ 0 0 sin 70 = sin (90 0 ) = cos 0 cos 70 = cos (90 0 ) = sin 0 04 sin (80 θ) = sin θ cos (80 θ) = cos θ tan (80 θ) = sin (80 θ) cos (80 θ) = sin θ cos θ = tan θ
4 0 tan (90 θ) = 7 tan θ = 7 tan θ = 7 0 sin 70 = sin (90 0 ) = cos 0 cos 70 = cos (90 0 ) = sin 0 sin 70 y 70 sin 0 0 (sin 0 cos 0 ) + (sin 70 + cos 70 ) = (sin 0 cos 0 ) + (cos 0 + sin 0 ) O cos 70 x = (sin 0 sin 0 cos 0 + cos 0 ) cos 0 + (cos 0 + sin 0 cos 0 + sin 0 ) = (sin 0 + cos 0 ) = 04 sin 60 = sin (80 0 ) = sin 0 cos 70 = cos (90 0 ) = sin 0 sin 70 = sin (90 0 ) = cos 0 sin 60 cos 70 + cos 0 sin 70 = sin 0 sin 0 + cos 0 cos 0 = sin 0 + cos 0 = 60 y sin 0 0 0 O x cos 0 sin 60 = sin(90 + 70 ) = cos 70 cos 0 = cos(90 70 ) = sin 70 70
4.4 05 tan 0 sin 0 cos 40 sin 5 06 cos 5 cos 50 sin 50 05 tan 0 sin 0 sin 5 cos 40 cos 0 > cos 40 > cos 45 06 cos 5 cos 50 sin 50 cos
4 05 tan 0 = sin 0 = sin 5 = sin 0 < tan 0 < sin 5 cos 0 > cos 40 > cos 45 > cos 40 > sin 0 < tan 0 < sin 5 < cos 40 06 sin 50 = sin (90 40 ) = cos 40 0 < θ < 90 θ cos θ cos 50 < cos 40 < cos 5 cos 5 cos 50 y O 45 40 0 x cos 45 cos 0 cos 40
4.5 07 sin θ + cos θ = sin θ cos θ =, sin 4 θ + cos 4 θ = 08 sin θ + cos θ = 0 θ 80 sin θ = 09 sin θ + cos θ = sin θ cos θ = tan θ + tan θ = 0 0 80 tan + tan = 0 sin + cos sin cos
4 07 sin θ + cos θ = sin θ cos θ sin 4 θ + cos 4 θ sin θ cos θ sin θ + cos θ sin θ cos θ 08 sin θ + cos θ = sin θ cos θ sin θ cos θ II 09 sin θ + cos θ = sin θ cos θ tan θ + tan θ = ( sin θ cos θ ) + ( cos θ sin θ sin θ cos θ 0 tan + tan ) sin + cos sin cos sin cos tan + tan = 0 sin cos sin + cos = (sin ± cos ) sin ± cos
4 07 sin θ + cos θ = sin θ + sin θ cos θ + cos θ = sin θ + cos θ = + sin θ cos θ = sin θ cos θ = sin 4 θ + cos 4 θ = (sin θ + cos θ) sin θ cos θ ( ) = = 08 sin θ + cos θ = cos θ = sin θ sin θ + cos θ = cos θ = sin θ cos θ sin θ + ( sin θ ) = sin θ sin θ 8 9 = 0 sin θ = t 9t t 4 = 0 t = ± + 4 9 4 8 0 θ 80 0 t sin θ = t = + 7 6 = ± 7 6 sin θ + cos θ = sin θ + sin θ cos θ + cos θ = 9 sin θ + cos = + sin θ cos θ = sin θ cos θ = 4 9 9 II sin θ cos θ t t 4 9 = 0 9t t 4 = 0
4 09 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 tan θ + ( tan θ = tan θ + tan θ ( = sin θ cos θ + cos θ sin θ ( = sin θ cos θ ) tan θ tan θ ) ( ) = sin θ + cos θ sin θ cos θ ) ( = 8 ) = 46 9 0 tan + tan = sin cos + cos sin = sin + cos cos sin = sin cos tan + tan = 0 sin cos = 0 sin cos = 0 (sin + cos ) = sin + sin cos + cos = + 0 = 8 5 (sin cos ) = sin sin cos + cos = 0 = 5 0 80 sin cos = 0 > 0 sin > 0 cos > 0 sin + cos > 0 sin + cos = 8 5 = 0 5 sin cos = ± 0 5 = ± 5
4.6 x 90 x 80 6 cos x + cos x = 0 cos θ + sin θ = 0 θ 0 < θ < 80 0 θ < 80 θ cos θ + sin θ cos θ = cos x + sin y = 4 sin x cos y = 4 0 x 80, 0 y 80 () sin x + cos y () x () y cos x cos x = t t t cos θ sin θ cos θ = sin θ sin θ sin θ cos θ sin θ cos θ cos θ tan θ \= 0 4 cos x + sin y sin x cos y sin x cos y
4 90 x 80 cos x 0 cos x = t 6t + t = 0 (t )(t + ) = 0 t 0 t = cos x = cos θ + sin θ = 0 x = 0 ( sin θ) + sin θ = 0 sin θ sin θ + = 0 sin θ = t 0 < θ < 80 0 < sin θ 0 < t t t + = 0 (t )(t ) = 0 t = sin θ =, 0 < θ < 80 θ = 0, 90, 50 cos θ = 0 cos θ \= 0 cos θ + sin θ cos θ = cos θ tan θ = sin θ cos θ + tan θ = cos θ + tan θ = + tan θ tan θ = 0, 0 θ < 80 θ = 0, 60
4 4 () cos x + sin y = ( sin x) + ( cos y) = (sin x + cos y) cos x + sin y = sin x + cos y = (sin x + cos y) = sin x + cos y + sin x cos y = + 4 = 0 x 80 sin x 0 sin x cos y > 0 sin x > 0 cos y > 0 sin x + cos y > 0 sin x + cos y = () sin x + cos y = sin x cos y = 4 4 = sin x( sin x) sin x sin x + 4 = 0 sin x = 0 x 80 x = 0, 50 () () cos y = sin x = = 0 y 80 y = 60
4.7 5 0 < θ < 5 sin θ cos θ > 0 6 cos θ + sin θ < 0 0 < θ < 80 7 0 θ < 90 cos θ = θ tan θ > θ < θ < 5 sin θ = cos θ cos θ 6 cos θ = sin θ sin θ 7 0 θ < 90 tan θ = θ 0 tan θ > θ
4 5 ( cos θ) cos θ > 0 cos θ = t t + t < 0 (t )(t + ) < 0 y 5 < t < < cos θ < 0 < θ < 5 60 < θ < 5 6 ( sin θ) + sin θ < 0 sin θ sin θ > 0 sin θ( sin θ ) > 0 60 O y 50 x sin θ < 0, sin θ > 0 < θ < 80 0 < θ < 50 0 O x 7 0 θ < 90 cos θ = θ = 0 y tan θ = θ θ = 0 0 θ < 90 tan θ > θ 0 < θ < 90 O 0 x
4.8 8 0 θ 80 cos θ + sin θ + sin θ 9 0 θ < 90 f(θ) = tan θ + sin θ + cos θ + = cos θ + = cos θ f(θ) = tan θ + sin θ + cos θ f(θ) = + + tan θ f(θ) = + cos θ + = ( cos θ ) + = θ = f(θ) 0 f(x) = sin x + a cos x + 0 x 80 () a = f(x) x () a 0 < a < f(x) 5 a () a a f(x) x f(x) x
4 8 cos θ = sin θ sin θ 0 θ 80 sin θ 0 sin θ 9 f(θ) cos θ 0 sin x = cos x f(x) cos x cos x = t t 0 x 80 t
4 8 sin x = t 0 θ 80 0 t cos θ + sin θ + sin θ = ( sin θ) + sin θ + sin θ = t + t + = (t ) + 0 t t = x = 90 t = 0 x = 0, 80 y max min O t 9 0 θ < 90 f(θ) = tan θ + sin θ + cos θ sin θ + cos θ = cos θ + tan θ = cos θ f(θ) = tan θ + sin θ + cos θ f(θ) = tan θ + ( cos θ) + cos θ = + cos θ + tan θ f(θ) = + cos θ + ( + tan θ) ( ) = + cos θ + cos θ = cos θ + cos θ cos θ cos θ = 0 f(θ) cos θ cos θ = 0 cos θ = 0 θ < 90 cos θ = θ = 0 f(θ)
4 0 f(x) = sin x + a cos x + = ( cos x) + a cos x + = cos x + a cos x + cos x = t 0 x 80 t ( f(x) = t + at + = t a ) + a 4 + = g(t) () a = ( g(t) = t ) + 9 4 t g(t) f(x) ( ) g = 9 4 0 θ 80 t = cos x = x = 60 9 4 y O max t () 0 < a < t = a 0 < a < t ( ) g(t) g a 5 y max a 4 + = 5 a = ( 0 < a < ) () a y = g(t) t = a O a t a t g(t) g() = a + g( ) = a + y a + max 0 θ 80 t = cos x = x = 0 t = cos x = x = 80 f(x) min O a + a t a + x 0 a + x 80
4. a b c H H H = H = H = H a = b a H c () = = = 60 = () = 0 = = = () = 5 = 8 = 7 cos
4 H sin = H, cos = H b b () x = b + c bc cos () () cos = c + a b b x c b b c ca b H b c () x x () a ()
4 H H = sin = b sin H = cos = b cos H = c b cos H a = H + H = b sin + (c b cos ) = b sin + c bc cos + b cos = b (sin + cos ) + c bc cos = b + c bc cos () = + cos 60 = 9 + 4 6 = 7 > 0 = 7 () = x = + x x cos 0 x x 0 = 0 (x 5)(x + ) = 0 x > 0 = 5 60 0 x () cos = 5 + 64 49 = 5 8 0 < < 80 = 60 = 5 8 sin 60 = 0 5 b 8 c H 7 a
4. 8 4 a < a < a < a < 4 = x, =, = 5 x () x () x () a b c a b < c < a + b a b b + c < a c 4 S S = = ab sin (= bc sin = ) ca sin c b S S = s(s a)(s b)(s c) s = a + b + c a
4 8 4 < a < 8 + 4 4 < a < 4 + 8 < a a > 4 5 4 5 < a < 4 a 8 4 () (x ) (5 x) < < (x ) + (5 x) x < < x < < x < 4 () = θ cos θ = + (5 x) (x ) (5 x) = (5 x) sin θ = 8 8x 4(5 x) = 7 x 5 x = (5 x) cos θ ( = (5 x) 7 x 5 x = (5 x) (7 x) = x + 8x 4 = (x ) + () < x < 4 x = ) x θ 5 x (x ) + + (5 x) s = = = s(s x + )(s )(s 5 + x) = (4 x) (x ) = x + 8x 4
4. 5 a = R sin R 6 () = 60 = () 4 4 sin ( + ) sin = = = () = 0 = 05 0 7 sin : sin : sin = 5 : 6 : 7 θ cos θ = 5 6 () () 4 + + 80 () 7 sin : sin : sin = a R : b R : c R = a : b : c
4 5 D D = D a = R sin D = R sin R O D 6 () R sin = R R = sin 60 = a 60 () + + = 80 sin ( + ) = sin (80 ) = sin 4 sin ( + ) sin = sin = 4 0 < < 80 0 < sin sin = = 60 0 R R = 4 sin = R = R sin = 4 = 4 () = 80 (0 + 05 ) = 45 sin 0 = sin 45 = sin 45 sin 0 = 0 = 5 7 R a sin = b sin = c = R sin sin = a R, sin = b R, sin = c R sin : sin : sin = 5 : 6 : 7 a : b : c = 5 : 6 : 7 t > 0 a = 5t b = 6t c = 7t c θ cos θ = a + b c = 5t + 6t 49t = ab 5t 6t 5 0 05 0
4.4 8 4 9 = 8 = 5 = 7 r 0 a, b, c, a b c () a () b c 8 9 I r = I + I + I = r + r + r = r ( + + ) 0 R r a = E + E = D + F = (c r) + (b r) r = b + c a r I r r b a c a E r r r c D b F
4 8 4 θ cos θ = + 4 0 < θ < 80 sin θ > 0 sin θ = cos θ = ( 4 = 4 ) = 5 4 R R = 4 R = sin θ sin θ = 4 = 8 5 5 5 9 cos = 8 + 5 7 = 8 5 S = 60 S = sin 60 = 8 5 = 0 r S = r ( + + ) r (8 + 7 + 5) = 0 r = 0 () a b c a a = = () b + c = r r = b + c = c = 4 b b + (4 b) = 9 b = 4 ± c = 4 b = 4 4 ± b c b = 4 + c = 4 = 4 b b a r c c
4.5 = 4 = 5 = 6 D D D = D = D = 4 = 4 D = 5 D = 9 O D = = D = = D = = 0 D > D = D = O sin D = D = + D = D
4 80 D D D D D 80 D D = 80 cos = cos (80 ) = cos D + D = D D D D D D 0
4 = θ cos θ = 4 + 5 6 = 4 5 8 D = x D = 80 θ D 6 = + x x cos(80 θ) 6 = 4 + x 4x( cos θ) x + x = 0 x = ± 57 4 x = D > 0 D = + 57 4 4 θ 5 6 x D D = α D D = 4 + 9 4 9 cos α = 97 7 cos α D = 80 α D D = 4 + 5 4 5 cos (80 α) = 4 + 40 cos α 97 7 cos α = 4 + 40 cos α cos α = D = 97 7 = 6 D = 6 α 4 9 4 5 80 α D = β D = 80 β D = 4 + 4 4 4 cos β = cos β = 5 + 9 5 9 cos (80 β) = 06 + 90 cos β 4 cos β = 74 cos β = 7 6 = ( + 7 ) 6 = 56 6 6 4
4 = + cos = 8 + 8 6 cos 0 = 4 > 0 = 6 D = = 80 0 = 0 0 x R sin 0 = R R = sin 0 = 6 = D R = D sin D sin D = D R = = D = = 0 D = x D ( ) = ( ) + x x cos 0 x 6x + 4 = 0 x = ± 5 D D D D = D = 0 = = D D D > D D = + 5, D = 5 D + D = sin + D D sin D = sin 0 + ( + 5)( 5) sin 60 6 4 D = (8 + 4) =
4.6 4 = a = b = c () a = b cos () sin = sin + sin () a = b + c + bc 5 a b c () a cos = b cos () a cos b cos = c 6 a = b = c = tan a = tan b
4 4 a b c () cos = a + b c ab a b c () sin = a R, sin = b R, sin = c R () a 5 cos a b c 6 tan cos sin a b c
4 4 () cos = a + b c ab a = b cos a = b a + b c ab a = a + b c b = c b > 0 c > 0 b = c b = c c a b () R a sin = b sin = c sin = R sin = a R, sin = b R, sin = c R sin = sin + sin ( ) a ( ) = b ( ) + c a = b + c R R R = 90 () a = b + c bc cos a = b + c + bc b + c bc cos = b + c + bc bc( + cos ) = 0 b \= 0 c \= 0 + cos = 0 cos = = 0
4 5 () a cos = b cos a cos = b cos a a + c b = b b + c a ac bc a + c b = b + c a c c a = b a > 0 b > 0 a = b a = b c a b () a cos b cos = c a a + c b b b + c a = c ac bc a + c b c b + c a c = c a + c b (b + c a ) = c a = b + c = 90 6 R tan a = sin a cos = a a R bc b + c a = bc a(b + c a )R tan b = b b R tan a = tan b bc a(b + c a )R = b a(b + c a ) = ac a + c b = ca b(a + c b )R ca b(a + c b )R a b(a + c b ) b (a + c b ) = a (b + c a ) c (b a )c (b 4 a 4 ) = 0 (b a )c (b + a )(b a ) = 0 (b + a)(b a){c (b + a )} = 0 b + a > 0 b = a c = a + b = = 90 c a b
4.7 7 () : = : = 7 = 60 5 () : : = : : 4 8 = 60 = c = b () () P P 9 () D = D = 5 = D = 7 D = 8 D () D = 60, = 75, D =, =, = 40 x cm cm cm
4 7 () sin = 60 : = : = x 60 = x = 7 x () : : = : : 4 = x = x = 4x 8 () b c () = P + P P 9 () D = D () 40 8
4 7 () : = : = x = x ( 7) = (x) + (x) x x cos 60 8 = 4x + 9x x x = 4 x = ( x > 0) x 7 60 x x sin 60 = 4 6 = 6 x () : : = : : 4 = x = x = 4x cos = (x) + (4x) (x) = 7 x 4x 8 x x 0 < < 80 sin > 0 4x sin = ( ) cos = 7 5 = 8 8 5 5 4x x 8 = = = 4 5 8 () = bc sin 60 = x = 4 9 4 bc () P = x () = P + P 4 bc = cx sin 0 + bx sin 0 bc bc = (b + c)x P = x = b + c P P x = c P : P = : = c : b cx sin 0 = c b + c bc sin 60 x = bc b + c ( x > 0) 0 0 x P b
4 9 () D cos = 5 + 7 8 = 5 7 7 0 < < 80 sin > 0 sin = ( ) cos = 4 = 7 7 D D = 5 7 4 = 0 7 () D = D = D = D = 75 0 = 45 S S = D + D = + sin 45 = + = 40 x 6 6 x x sin 60 = x (cm ) r O = O = r = x O = 45 O x = r + r r r cos 45 x = ( )r r = x = + 8 O = 8 r sin 45 = + = ( + )x (cm ) ( x + x + x x ) 4 ( ) x = ( + ) x x = ( + )x (cm ) x D 5 7 8 7 5 D 60 0 45 x x r r 45 O x O x
4.8 4 P Q R S QR PQS : : Q P R S 4 D E D EF DEF EF S D S : = : F S : S = : 4 S T S : T 44 DE F G H I J () H H I H : H = : J () IH I IH : I = : F () FGHIJ DE FGHIJ : DE = : H G D E
4 4 a : b a : b 4 D EF : = E : DEF = E E = = a E = x 4 O 6 ( ) 44 () D ED I H E = 80 5 = 6 = 08 6 H () IH H I D E
4 4 QR PS : : QR : PS : = : : R S QR : QRS = : 9 QR = PQS = PS QR QRS = 4 = QR : PQS : = : : 9 P Q R S 4 = = a E = x D EF a : = : x ax = F + F = x + = a x a(a ) = a a = 0 a > 0 a = + 5 : = : a = : + 5 D EF S : S = : a + 5 = : x E D F a
4 4 O D O a : D = : D = a : a tan 0 = : ( = : ) S : T = ( ) : = : 4 O D 0 44 DE D ED 80 E = 80 5 = 08 I = I = 80 08 IH = HI = 7 () H : H = 6 : 7 = : () IH = I = x IH H H = I = I IH : H = H : H : x = x : (x + ) = 6 x x = 0 x = + 5 + 5 IH : I = : I H ( x > 0) () FGHIJ DE IH = = H = + x = + 5 ( ) + 5 : = : 7 + 5 J I F H G D E
4.9 45 0m 57 m m 67 m tan 57 =.599 tan 67 =.559 46 60 00m 0 m m 47 cm 4cm 4cm = α sin α =, cos α = 4 4 48 D EFGH = D = E = D DE = θ () D DE E H G () cos θ E F () DE (4) DE
4 45 46 47 48 (4) DE E D h DE
4 45 m x m tan 57 = x 0 x = 0 tan 57 = 0.599 = 46.97 x + = 47.97 47 (m) m 57 0m xm 67 m y m y = 0 tan 67 = 0.559 = 70.677 y + = 7.677 7 (m) 46 H = x H = x tan 60 = x = H tan 0 = H = x + = x + 00 = 9x x > 0 x = 00 8 = 00 = 5 = x = 5 (m), H = 5 6 (m) H 60 0 xm 00m 47 = 4 = 4 + = 5 4 5 = 0 (cm ) = 4 + 5 = 4 sin α = = 5 4, cos α = 4 = 4 4 4 4 α 5
4 48 () D = + = DE = + = 5 E = + = 0 () DE cos θ = ( 5) + ( 0) ( ) 5 0 = 5 E D D 5 F G = 0 () 0 < θ < 80 sin θ > 0 sin θ = ( cos θ = 0 ) = 7 0 E θ 0 DE = 5 0 7 0 = 7 (4) DE V V = E D D = = h H G DE h V = h DE E F = h 7 = 7 6 h = 7 6 h h = 6 7
4.0 49 = = D = = D = D = 5 D D D 50 OD O = O = O = OD = = = D = O D = 4 cm M OD M D OD cm M 5 = cm D = N D 6 cm E = cm D R M EFGH D E : M N FG H Q EH P Q S MN R F P G EG PQ S () () () MR () MR PGS
4 49 D = = D D 50 a : b a : b V ( ) V = ( OD ) ( ) = ( OD ) 5 () MR : () G SR PM
4 49 D = θ D cos θ = + ( 5) = 0 < θ < 80 sin θ > 0 sin θ = ( ) cos θ = 5 = D R D R = D 5 R = = sin θ 5 D H H = H = 9 H H = H = 9 H DH = D H = 9 H H = H = DH H D H = R = H = H = 9 9 4 = D D H = 5 = 5 5 5 H D D D = D + D D = 90 D R R = =
4 50 OD O V ( ) V = OD = 8 OD O D H H = = 4 + 4 = OH = O H = 4 ( ) M 4 H O D = V = 6 4 = (cm ) H 5 () MR MR : = M : = : = : MR = = cm () G SR PM T TMR TPGS M : PG = : : = 8 : 7 ( V V = 8 ) TPGS 7 PGS = PG PS = = 9 4 TG = h T : TG = : (h ) : h = : h = (h ) h = 9 TPGS = PGS h = 9 4 9 = 7 4 V = 9 7 7 4 = 9 4 (cm ) P M S R T G
4. 5 D M MD = θ cos θ = MD θ D M 5 O O P P = θ cos θ = 5 OP < P OP 54 O O : P O P = θ P S () P () cos θ = S = () O V P θ h V = (4) O P h
4 5 4 M M DM D MD M = DM MD cos θ cos θ sin θ 5 P P = P cos θ 54 () O H O = O = O H H = H sin 60 = H H = (4) OP h
4 5 M DM M = DM = sin 60 = MD cos θ = ( ) + ( ) = 0 < θ < 80 sin θ > 0 sin θ = ( ) cos θ = = MD = = M θ D 5 P = x P = P P cos θ = x + x x x cos θ = 5 x x = 5 6x = 0x x = 6 = x x P = x = ( x > 0) 4 OP = 60 OP = y OP ) = + y y cos 60 ( 4 y y + 6 = 0 (4y )(4y ) = 0 OP = y = ( y < ) 4 P y θ x O x
4 54 () P ( ) P = + 4 4 cos 60 = 6 P = ( P > 0) 4 () P = P = 4 cos θ = P + P P P P = 5 0 < θ < 80 sin θ > 0 ( ) sin θ = 5 = P S S = 4 4 = 8 P θ 4 O () O OH H H M H M O H = M = sin 60 = ( ) 6 OH = = P M O V H V = OH = 6 sin 60 = (4) OP V OP : P = : V = V 4 = 4 = 6 V = S h = h 8 h 8 = 6 h = P O h
4. 55 a D 56 DE P Q P DE Q DE P Q DE () () P () Q E Q P D 57 = 6 = 6 O O 58
4 r V = 4 πr, S = 4πr r 55 D 56 57 58
4 55 D H = = D H D D H D D M H M H = a sin 60 = a ( ) 6 H = a a = a O R 6 OH = a R H + HO = O ( ) ( ) 6 a + a R = R 6 R = 4 a M MO M O : OH = M : MH = : R = O = 4 H = 6 4 a 56 () F DE F = F = = 4 = F + F = 4 + = 7 () ED G F G P Q FH = FG = = R H R H E O M M G D D H = F FH = 4 = 5 F
4 P r FH PI F : P = FH : PI 4 : ( 5 r) = : r 4r = 5 r r = 5 5 () J = H r = 5 5 = 5 5 5 J : H = 5 : 5 = : 5 5 Q P QJ : PH = : 5 ( Q = 5 F H ) ( ) P = 4 5 π r ( ) 5 = 4 5 5 5 5 π = 08 5 5 π = 4π 5 I Q J P G 57 6 G M GM = M tan 0 = = O = 4 π( ) = 4 π G G M 0 M 58 O r OH = r O = r OH r = (r ) + r = 5 4 π r = 5 6 π H r O r