Identify the point on the unite circle coressponding to an angle of 300 degrees in standard position
A (-√3, -√3/2)
B (-√3/2, 1/2)
C (1/2, -√3/2)
D (1/2, -√3 )
I don't get how to figure this out :|
Ask yourself, "Which quadrant does 300° fall in" ?
It is in quadrant IV
what does a typical point in quadrant IV look like?
it must be of the type (+ , - )
the only points with that combination is D (1/2,-√3) or C(1/2 , -√3/2)
check:
remember tanØ = y/x
tan 300° = -1.732.. = -√3
for D) : -√3 / (1/2) ≠ -√3
for C) : (-√3/2) / (1/2) - -√3
so it is point C
Oh that makes sense, thank you :)
To find the point on the unit circle corresponding to an angle of 300 degrees in standard position, you can use the following steps:
1. Convert the angle from degrees to radians. Since the unit circle is commonly used in radians, we need to convert 300 degrees to radians. Recall that π radians is equivalent to 180 degrees. Therefore, we can write:
300 degrees = (300/180) * π radians
Simplifying this expression gives:
300 degrees = (5/3)π radians
2. Use the radian value obtained in step 1 to determine the coordinates on the unit circle. The x-coordinate and y-coordinate of a point on the unit circle can be found using the following trigonometric formulas:
x = cos(θ)
y = sin(θ)
In our case, θ represents the angle in radians, so we substitute (5/3)π into these formulas:
x = cos((5/3)π)
y = sin((5/3)π)
3. Evaluate the trigonometric functions using the reference angles. For angles greater than 2π or 360 degrees, we can use the reference angle to determine the coordinates on the unit circle. The reference angle for (5/3)π radians is (5/3)π - 2π, which simplifies to (5/3)π - (6/3)π = -π/3 radians.
Now we have:
x = cos(-π/3)
y = sin(-π/3)
4. Evaluate the trigonometric functions using the unit circle values. For angles close to the x-axis (0, 2π, etc.) or the y-axis (π/2, 3π/2, etc.), we can use the values of cos(θ) and sin(θ) from the unit circle.
The unit circle values for -π/3 radians are:
cos(-π/3) = 1/2
sin(-π/3) = -√3/2
Therefore, the coordinates on the unit circle for an angle of 300 degrees in standard position are (1/2, -√3/2).
Looking at the options given, the correct answer is C (1/2, -√3/2).