Question

Question 7 (9 points) Find all solutions in the interval [0, 360°). sin(5x) = 0 15°, 30°, 1050, 120°, 1950, 2100, 2850, 3000 O 75°, 105°, 255°, 285° 45°, 90°, 135°, 180°, 225°, 0°, 36º, 72°, 108°, 144°, 180 FOR 0 xo

Answer 1

7 =180° n=0,1,2,- sin (5x) = 0 sin (5x) = sin (not) where 5x = nx180° x = nx180° _nx360 Пт 5 א when א wo x =0 x = 36 x x = 1080 72. א n=2 n=3 n=4 x = 1440 n=5 , x=180° n=6 x=216 n=7, 2= 2526 nad 2 = 2880 n=9 , x= 324° א O a=5 b= 8. C=310 cosine Law cr= a + b - rab Cosc = 0 5+ 8 - 2 x S x 8 CB 310 = 25+64 – 80 CB310 = 89 - 68.576 = 20.42 4 c= /20.424 = 4.52 al CB31= 8572 Let I sin (arc tana) = sin (tant (2)) = sin (sin" (12/4)) tan (2) = x tanx=2 sina = 2 = x= sin (

Answer 2

ANSWERS :

7.

sin(5x) = 0. ; x in the interval [ 0, 360º) 

So, 

5x = 0, pi, 2pi, 3pi, 4pi 5pi, 6pi, 7pi, 8pi, 9pi 

=> x = 0º, 36º, 72º, 108º, 144º, 180º, 216º, 252º, 288º, 324º  : 4th option (ANSWER).

8.

As per cosine law :

c = sqrt(a^2 + b^2 - 2 a b cos (b)) = sqrt(5^2 + 8^2 - 2 * 5 * 8 cos(31)) = 4.52 

So, c = 4.52 (ANSWER).

9.

arcsin(-0.90) = asin(- 0.90) = - 1.1198 radians 

= (3.1416 + 1.1198) or (6.2832 - 1.1198) radians in the interval (0, 2 pi) 

= 4.2614 (or 5.634) ( radians in the interval (0, 2 pi) ).  (ANSWER).

10.

tan^-1 (26) = arctan(26) = atan(26) = 87.80º (ANSWER).

11.

Arccos (- 0.60) = acos(-0.60) = 2.2143 radians (ANSWER).

12.

Let sin(arctan(2)) = sin(x)

=> arctan (2) = x

=> 2 = tan(x) = sin(x) / cos(x)

=> 2 cos(x) = sin(x)

Squaring :

=> 4 cos^2 (x) = sin^2 (x)

=> 4( 1 - sin^2(x)) = sin^2 (x)

=> 5 sin^2(x) = 4

=> sin^2 (x) = 4/5

=> sin(x) = 2/sqrt(5) 

=> sin(x) = 2 sqrt(5) / 5 : 4th option (ANSWER).