P (-V3/2, -1/2 and Q(1/2, V3/2 are two points on the unit circle. If an object rotates counterclockwise from point P to point Q, what angle has it rotated?
180 + 60 = 330 P
60 Q
I got like 300, but its supposed to be 210 degrees:\
Untamed,
I have now answered several rather straightforward trig questions for you.
You label your subject as Calculus.
You should know this stuff, in most jurisdictions this is considered grade 10 material or below
I suggest you graph your points , draw the lines and find the angle each line makes with the x-axis.
e.g for Q , tan(angle) = (√3/2) / (1/2) = √3
angle with x=axis is 60° (because tan60 = √3)
etc
It should be easy to see that it is 210°
Sorry, I just really suck at trigonmetry, and Im in grade 11.
So, did you follow my suggestion above, and did you get 210° ?
To find the angle that the object has rotated from point P to point Q on the unit circle, you can use the concept of the Cartesian coordinate system and trigonometry.
Firstly, let's label the points on the unit circle:
Point P: (-√3/2, -1/2)
Point Q: (1/2, √3/2)
The x-coordinate represents the cosine of the angle, and the y-coordinate represents the sine of the angle.
Now, let's calculate the angles using trigonometry.
For point P:
cos(θ) = -√3/2
sin(θ) = -1/2
Using the inverse cosine function, we can find the angle θ:
θ = arccos(-√3/2)
For point Q:
cos(φ) = 1/2
sin(φ) = √3/2
Similarly, using the inverse cosine function, we can find the angle φ:
φ = arccos(1/2)
Now, to identify the angle of rotation from P to Q, we can calculate φ - θ:
angle = φ - θ
Substituting the values of θ and φ:
angle = arccos(1/2) - arccos(-√3/2)
Using trigonometric properties and identities, the expression can be simplified:
angle = 60° - 150°
angle = -90°
Since we are considering the counterclockwise direction, we can convert the negative angle to a positive angle:
angle = 360° - (-90°)
angle = 360° + 90°
angle = 450°
Therefore, the object has rotated 450 degrees counterclockwise from point P to point Q on the unit circle.