Asksia AI LOGO

Sia

rx's Question
Math
Posted about 2 months ago

An angle in standard position in the xy\boldsymbol{x} \boldsymbol{y}-plane is given in radians. A circle is centered at the origin with the given radius.
What are the coordinates of the point of intersection of the terminal ray of the angle and the circle? *
[4) (1分)
θ\theta
=π2,r=\frac{\pi}{2}, r \qquad
9
Sign in to unlock the answer
Answer from Sia
Posted about 2 months ago
Solution by Steps
step 1
To find the radius r r , we use the distance formula from the origin to the point (82,82) (-8\sqrt{2}, -8\sqrt{2}) : r=(82)2+(82)2 r = \sqrt{(-8\sqrt{2})^2 + (-8\sqrt{2})^2}
step 2
Calculating r r : r=128+128=256=16 r = \sqrt{128 + 128} = \sqrt{256} = 16
step 3
To find the angle θ \theta , we use the tangent function: tan(θ)=yx=8282=1 \tan(\theta) = \frac{y}{x} = \frac{-8\sqrt{2}}{-8\sqrt{2}} = 1
step 4
Since the point (82,82) (-8\sqrt{2}, -8\sqrt{2}) is in the third quadrant, we take θ=5π4 \theta = \frac{5\pi}{4}
Answer
r=16 r = 16 and θ=5π4 \theta = \frac{5\pi}{4}
Key Concept
The relationship between the coordinates of a point and the radius and angle in polar coordinates.
Explanation
The radius is determined by the distance from the origin to the point, and the angle is found using the tangent function, adjusted for the quadrant.

Not the question you are looking for? Ask here!

Enter question by text

Enter question by image

Unlock Smarter Learning with AskSia Super!

Join Super, our all-in-one AI solution that can greatly improve your learning efficiency.

30% higher accuracy than GPT-4o
Entire learning journey support
The most student-friendly features
Study Other Question