How do you solve 10sin(x-2)=-710sin(x−2)=−7?

1 Answer
Nghi N.
Sep 15, 2016

70^@22 and 339^@0870∘22and339∘08 for (0, 360)

Explanation:

First convert 2 radian to degrees
3.14 --> 180^@
1 radian --> 180/(3.14)
2 radian --> (2(180))/3.14 = 360/3.14 = 114^@652(180)3.14=3603.14=114∘65
The equation becomes:
10sin(x - 114.65) = - 7
sin (x - 114.65) = -7/10 = - 0.7
Calculator and unit circle -->
Arc (x - 114.65) = - 44^@43(x−114.65)=−44∘43
arc (- 44.43) is co-terminal to arc (360 - 44.43 = 315^@57)(360−44.43=315∘57)
and arc x - 114.65 = 180 + 44.43 = 224^@43x−114.65=180+44.43=224∘43
a. x - 114.65 = 224.43 --> x = 339^@08x=339∘08
b. x - 114.65 = 315.57 --> x = 430^@32x=430∘32, or 70^@2270∘22
Answer for (0, 360):
70^@22; 339^@0870∘22;339∘08

Related questions
See all questions in Solving Trigonometric Equations
Impact of this question
1578 views around the world
You can reuse this answer
Creative Commons License