14.4k views
4 votes
100 POINTS! NEED HELP QUICKLY! Look at picture below

100 POINTS! NEED HELP QUICKLY! Look at picture below-example-1

1 Answer

5 votes

Answer:

60, 75

150 165

240 255

330 345

Explanation:

csc 4 theta = -2 sqrt(3)/3

Write in terms of sin

1/ sin (4 theta) = -2 sqrt(3)/3

Using cross products

-2 sqrt(3) = 3 sin (4 theta)

Divide each side by 3

-2 sqrt(3)/3 = sin (4 theta)

Take the inverse sin on each side

sin ^ -1(-2 sqrt(3)/3) = sin ^ -1 (sin (4 theta))

240 +360n = 4 theta

and 300 +360n = 4 theta where n is an integer

Dividing each side by 4

240/4 +360n/4 = 4/4 theta and 300/4 +360n/4 = 4/4 theta

60 + 90n = theta and 75 +90n = theta

We want all the values between 0 and 360

Let n=0

60, 75

n=1

60+90=150 and 75+90 =165

n=2

60+180= 240 75+180=255

n=3

60+270 = 330 75+ 270 =345

User Shantal
by
7.3k points