Check this for me involving sin theta

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In summary, for the given equation sin theta= -0.4321, with a range of 0<=theta<=2pi, there are 2 possible solutions found in quadrants 3 and 4. The reference angle is -26 degrees, and the solutions to the equation are theta=334 degrees and theta=206 degrees, both rounded to the nearest degree. The accuracy of the reference angle may need to be confirmed.
  • #1
aisha
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Check this for me please involving sin theta

For sin theta= -0.4321, 0<=theta<=2pi

QUESTIONS

a) How many solutions are possible?
b)In which quadrants would you find the solutions?
c)Determine the reference angle for this equation to the nearest degree.
d) Determine all the solutions to the equation to the nearest degree

MY ANSWERS

a) 2
b) quadrants 3 and 4
c)-26 degrees (im not sure if the negative should be there)
d)solutions theta=334 degrees and theta=206 degrees

Can someone please check to see if I am on the right track please
 
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  • #2
I don't know what they mean by reference angle (you may want to consult the book),but the rest looks perfect to me...:smile: :wink:

Daniel.
 
  • #3
Thanks does anyone know if the reference angle is correct or not if its not then the solutions should be wrong too :approve:
 
  • #4
The solutions (point "d") are correct,no doubt about it...:wink:

Daniel.
 

What is the meaning of "sin theta"?

Sin theta, often written as sin θ, is a mathematical function that represents the ratio of the side opposite an angle in a right triangle to the hypotenuse of the triangle.

How do you calculate the value of sin theta?

The value of sin theta can be calculated using a scientific calculator or by using a trigonometric table. It can also be calculated by dividing the length of the side opposite the angle by the length of the hypotenuse in a right triangle.

What are the applications of sin theta in science and mathematics?

Sin theta is used in various fields of science and mathematics, such as physics, engineering, and astronomy. It is used to calculate the position, velocity, and acceleration of objects in motion, as well as in the study of waves and periodic phenomena.

What are some common mistakes when using sin theta?

Some common mistakes when using sin theta include forgetting to convert the angle to radians, using the wrong angle in relation to the triangle, and not understanding the difference between sine and cosine functions.

Can sin theta be negative?

Yes, sin theta can be negative. It is negative in quadrants III and IV of the unit circle, where the y-coordinate is negative. It can also be negative in certain applications, such as when calculating the direction of a vector.

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