1. Find the angle of smallest positive measure coterminal with an angle of the given measure:
a. 520
b. - 75
2. Points A (1,0) and B (.6,-.8) are points on a unit circle O. If the measure of angle AOB = 0 {w/ a line in the middle}
Find
a. sin 0
b. cos 0
c. tan 0
Ok I understand the first one. I have to subtract 520 - 360 = 160. But for the second question, I'm confused but I know x is always cos and y is always sin. I don't know how to use that to find sin 0 and etc.
Now thinking about it, should i use the distance formula for both of these two coordinates. I'm a little confused about this.
1. To find the angle of smallest positive measure coterminal with an angle of the given measure, you can add or subtract multiples of 360 degrees (or 2π radians) until you get a positive angle less than 360 degrees.
a. For angle 520 degrees, you can subtract 360 degrees to find the smallest positive coterminal angle:
520 degrees - 360 degrees = 160 degrees
The angle of smallest positive measure coterminal with 520 degrees is 160 degrees.
b. For angle -75 degrees, you can add 360 degrees to find the smallest positive coterminal angle:
-75 degrees + 360 degrees = 285 degrees
The angle of smallest positive measure coterminal with -75 degrees is 285 degrees.
2. Given points A(1,0) and B(0.6,-0.8) on a unit circle, the angle AOB is the angle formed between the positive x-axis and the line segment joining points A and B.
a. To find sin θ, where θ is the angle AOB, you can use the y-coordinate of point B divided by the radius of the unit circle:
sin θ = y-coordinate / radius
In this case, the y-coordinate of point B is -0.8, and the radius of the unit circle is 1:
sin θ = -0.8 / 1 = -0.8
b. To find cos θ, you can use the x-coordinate of point B divided by the radius of the unit circle:
cos θ = x-coordinate / radius
In this case, the x-coordinate of point B is 0.6, and the radius of the unit circle is 1:
cos θ = 0.6 / 1 = 0.6
c. To find tan θ, you can use the y-coordinate divided by the x-coordinate of point B:
tan θ = y-coordinate / x-coordinate
In this case, the y-coordinate of point B is -0.8 and the x-coordinate is 0.6:
tan θ = -0.8 / 0.6 = -1.3333 (rounded to four decimal places)
So,
a. sin θ = -0.8
b. cos θ = 0.6
c. tan θ = -1.3333 (rounded to four decimal places)
1. To find the angle of smallest positive measure coterminal with an angle of the given measure:
a. For angle 520, we need to find the equivalent angle between 0 and 360 degrees. To do this, subtract multiples of 360 from the given measure until you obtain an angle that is between 0 and 360.
520 - 360 = 160 degrees
Therefore, the angle of smallest positive measure coterminal with 520 degrees is 160 degrees.
b. For angle -75, we need to find the equivalent angle between 0 and 360 degrees. To do this, add multiples of 360 to the given measure until you obtain an angle that is between 0 and 360.
-75 + 360 = 285 degrees
Therefore, the angle of smallest positive measure coterminal with -75 degrees is 285 degrees.
2. To find the values of sine, cosine, and tangent for a given angle on a unit circle:
a. The sine of an angle is the y-coordinate of the point where the terminal side of the angle intersects the unit circle. In this case, the angle AOB is 0 degrees and the point B has coordinates (.6, -.8). Hence, sin 0 is equal to the y-coordinate of point B, which is -0.8.
Therefore, sin 0 = -0.8.
b. The cosine of an angle is the x-coordinate of the point where the terminal side of the angle intersects the unit circle. In this case, the angle AOB is 0 degrees and the point B has coordinates (.6, -.8). Hence, cos 0 is equal to the x-coordinate of point B, which is 0.6.
Therefore, cos 0 = 0.6.
c. The tangent of an angle is equal to the ratio of sine to cosine. In this case, tan 0 can be calculated by dividing sin 0 (-0.8) by cos 0 (0.6).
tan 0 = -0.8 / 0.6 = -1.33 (approximately).
Therefore, tan 0 = -1.33.