10.4k views
4 votes
Use trigonometric identities to solve the trigonometric equation sin(2∅)-cos(∅)=0 for 0≤∅≤2π. You must show all of your work analytically.

User Duc Filan
by
7.3k points

1 Answer

7 votes

Explanation:

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

2sin(x)cos(x) - cos(x) = 0

so one solution is cos(x) = 0.

=> x = pi/2 and 3pi/2 (90° and 270°)

for cos(x) <> 0 we have then

2sin(x) - 1 = 0

2sin(x) = 1

sin(x) = 1/2

=> x = pi/6 and 5pi/6 (30° and 150°)

User Droidman
by
7.3k points

Related questions

asked Dec 17, 2020 105k views
Qwe Asd asked Dec 17, 2020
by Qwe Asd
8.2k points
1 answer
5 votes
105k views