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frozenolaf1
@frozenolaf1
July 2022
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сделайте 452 пожалуйста
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oganesbagoyan
Verified answer
452
а) sinα=0,2 ; 0<α<90°.
----
cosα -?
cos²α+sin²α=1⇒cosα= ±√(1-sin²α) ,но т.к. 0<α<90°,где cosα >0 ,то:
cosα= √(1-sin²α) =√(1-(0,2)²=√(1-(1/5)²)=√(1-1/25)=√(24/25)=√(4*6/25)= (2/5)√6=0,4√6.
--- или
cosα= √(1-sin²α)= √(1-(0,2)²=√(1-0,04) =√0,96 =√(0,16 *6) =0,4
√6.
-----------------
б) cosα=1.3 ; 0<α<90°.
----
sinα -?
cos²α+sin²α=1⇒sinα= ±√(1-cos²α) ,но т.к. 0<α<90°,где sinα >0 ,то:
sinα= √(1-cos²α)= √(1-(1/3))²=√(1-1/9) =√(8/9) =(2/3)√3
.
-----------------
в) sinα =(3/4)*cosα ⇒tqα=3/4 ; cosα =±1/√(1+tq²α) =±1/√(1+(3/4)²) =
= ±1/√(1+9/16) = ±1/√(25/16) = ±4/5 .
Если cosα= -4/5 ,то sinα=(3/4)*cosα=(
3/4)*(-4/5) = -3/5.
Если cosα= 4/5 ,то sinα=(3/4)*cosα=(
3/4)*(4/5) = 3/5.
------- или -------
а) cosα <0 ⇒sinα<0 .
---
sinα = - (3/4)*
√(1-sin²α) .⇔(-4sinα) =3√(1-sin²α) ⇔16sin²α =9(1-sin²α)⇒
sin²α =(3/5)² ⇒sinα = -3/5 , т.к.sinα<0 ; cosα= -4/5.
б) cosα > 0
⇒sinα>0 .
---
sinα = (3/4)*√(1-sin²α) .⇔(4sinα) =3√(1-sin²α) ⇔16sin²α =9(1-sin²α)⇒
sin²α =(3/5)² ⇒sinα = 3/5 , т.к.sinα>0 ; cos
α= 4/5.
ответ: sinα = -3/5 ; cosα = - 4/5 или sinα = 3/5 ; cosα =
4/5.
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Answers & Comments
Verified answer
452а) sinα=0,2 ; 0<α<90°.
----
cosα -?
cos²α+sin²α=1⇒cosα= ±√(1-sin²α) ,но т.к. 0<α<90°,где cosα >0 ,то:
cosα= √(1-sin²α) =√(1-(0,2)²=√(1-(1/5)²)=√(1-1/25)=√(24/25)=√(4*6/25)= (2/5)√6=0,4√6.
--- или
cosα= √(1-sin²α)= √(1-(0,2)²=√(1-0,04) =√0,96 =√(0,16 *6) =0,4√6.
-----------------
б) cosα=1.3 ; 0<α<90°.
----
sinα -?
cos²α+sin²α=1⇒sinα= ±√(1-cos²α) ,но т.к. 0<α<90°,где sinα >0 ,то:
sinα= √(1-cos²α)= √(1-(1/3))²=√(1-1/9) =√(8/9) =(2/3)√3.
-----------------
в) sinα =(3/4)*cosα ⇒tqα=3/4 ; cosα =±1/√(1+tq²α) =±1/√(1+(3/4)²) =
= ±1/√(1+9/16) = ±1/√(25/16) = ±4/5 .
Если cosα= -4/5 ,то sinα=(3/4)*cosα=(3/4)*(-4/5) = -3/5.
Если cosα= 4/5 ,то sinα=(3/4)*cosα=(3/4)*(4/5) = 3/5.
------- или -------
а) cosα <0 ⇒sinα<0 .
---
sinα = - (3/4)*√(1-sin²α) .⇔(-4sinα) =3√(1-sin²α) ⇔16sin²α =9(1-sin²α)⇒
sin²α =(3/5)² ⇒sinα = -3/5 , т.к.sinα<0 ; cosα= -4/5.
б) cosα > 0 ⇒sinα>0 .
---
sinα = (3/4)*√(1-sin²α) .⇔(4sinα) =3√(1-sin²α) ⇔16sin²α =9(1-sin²α)⇒
sin²α =(3/5)² ⇒sinα = 3/5 , т.к.sinα>0 ; cosα= 4/5.
ответ: sinα = -3/5 ; cosα = - 4/5 или sinα = 3/5 ; cosα = 4/5.