A.If 0 is less than or equal to thita is less than 360 ,find all possible value of thita such that :
1.Sin thita =0.5623
theta, not thita. I'll just use x. You want
sin x = 0.5623
Since sin is positive in QI and QII, and sin(34.2°) = 0.5623
the solutions are
x = 34.2° and 180-34.2°
Help some more am very much behind
To find all possible values of theta such that sin theta is equal to 0.5623, we can use the inverse sine function or the arcsin function.
Step 1: Take the inverse sine (arcsin) of 0.5623 to find one solution.
arcsin(0.5623) ≈ 34.4566°
Step 2: Since sin theta has both positive and negative values, we can find the second solution by subtracting the angle found in step 1 from 180°.
180° - 34.4566° ≈ 145.5434°
So, the two possible values of theta such that sin theta = 0.5623 are approximately:
1. Theta ≈ 34.4566°
2. Theta ≈ 145.5434°
To find all possible values of theta (θ) such that sin(theta) = 0.5623, we can use the inverse sine function (sin^(-1)) or arcsin.
Step 1: Take the inverse sine (or arcsin) of 0.5623:
arcsin(0.5623) = 33.8826 degrees (rounded to 4 decimal places).
Step 2: Since sin(theta) is a periodic function with a period of 360 degrees, we need to consider all possible angles within one complete revolution (360 degrees).
Step 3: To find additional angles, we can use the fact that sine is positive in the first and second quadrants.
In the first quadrant (0 to 90 degrees), we already have the angle 33.8826 degrees.
In the second quadrant (90 to 180 degrees), the angle 180 - 33.8826 = 146.1174 degrees is included.
Step 4: To take into account the full range of 360 degrees, we can subtract and add multiples of 360 degrees:
- First quadrant: 33.8826° + 360°n (where n is an integer)
- Second quadrant: 146.1174° + 360°n (where n is an integer)
Therefore, all possible values of theta such that sin(theta) = 0.5623 are given by:
Theta = 33.8826° + 360°n and Theta = 146.1174° + 360°n
where n is an integer representing additional revolutions.
For example, some possible theta values include:
- First quadrant: 33.8826°, 393.8826°, 753.8826°, ...
- Second quadrant: 146.1174°, 506.1174°, 866.1174°, ...
Note: It's important to keep in mind that angles can be measured in degrees or radians, so the answer can be expressed accordingly depending on the given angle unit.