if theta is an angle in standard position and B(-3,4) is a point on the terminal side of the angle, what is the value of sin theta?
B(-3,4), Q2.
r^2 = (-3)^2 + 4^2 = 25,
r = 5.
sinAr = Y/r= 4 / 5 = 0.8,
Ar = 53.1deg = reference angle.
sinAr = Y/r = 4 / 5 = 0.80,
Since the angle is in Q2,the angle
calculated is actually the ref angle
which has the same trig ratios as the
actual angle. The actual angle is:
A = 180 - Ar = 180 - 53.1 = 126.9deg.
sin126.9 = 0.8 = sin53.1.
To calculate the value of sin theta, we need to find the ratio of the y-coordinate of point B to the distance from the origin to point B.
The y-coordinate of point B is 4.
To find the distance from the origin, we can use the Pythagorean theorem:
Distance = sqrt((-3)^2 + 4^2)
Distance = sqrt(9 + 16)
Distance = sqrt(25)
Distance = 5
Now, we can calculate the sin theta:
sin theta = y-coordinate / distance
sin theta = 4 / 5
sin theta = 0.8
Therefore, the value of sin theta is 0.8.
To find the value of sin θ, we need to determine the ratio of the y-coordinate of point B to the distance from the origin to point B (also known as the radius or magnitude).
Given that point B has coordinates (-3,4), we can use the Pythagorean theorem to find the magnitude:
Magnitude = √((-3)^2 + 4^2)
= √(9 + 16)
= √(25)
= 5
So, the magnitude is 5.
Now, since sin θ is equal to the y-coordinate divided by the magnitude, we can calculate it:
sin θ = y-coordinate / magnitude
= 4 / 5
= 0.8
Therefore, the value of sin θ is 0.8.