1. Write the expression as a function of an acute angle whose measure is less than 45.
a. sin 80
b. sin (-100)
To find the postive acute angle, usually you would subtract 360 from the given measure. Would you have to subtract 45 from the given measure.
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
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.
I really need help on this. Its just two problems I have. I'm extremely confused on only these two problems. I would appreciate it a lot if someone can help me. This would be the last time I ask help for math. Thanks a lot.
1. To write the expression as a function of an acute angle whose measure is less than 45 degrees, you would have to use the concept of reference angles.
a. For sin 80 degrees: Since 80 degrees is already less than 90 degrees, the reference angle is simply 80 degrees.
So, the expression as a function of an acute angle whose measure is less than 45 degrees is sin 80 degrees.
b. For sin (-100) degrees: To find the positive acute angle, you subtract 360 from the given measure until you get an angle between 0 and 360 degrees.
-100 - 360 = -460 degrees
Since -460 degrees is greater than -540 degrees (which is -180 degrees subtracted from 360 degrees), you subtract -180 degrees from -460 degrees.
-460 - (-180) = -280 degrees
Now, since -280 degrees is greater than -360 degrees, you subtract -360 degrees from -280 degrees.
-280 - (-360) = -280 + 360 = 80 degrees
Therefore, the positive acute angle less than 45 degrees is 80 degrees.
So, the expression as a function of an acute angle whose measure is less than 45 degrees is sin 80 degrees.
2. Points A(1,0) and B(0.6, -0.8) are points on a unit circle O.
a. To find sin 0 degrees:
Since 0 degrees lies on the x-axis of the unit circle, the y-coordinate of the point A (1,0) gives us the sine value.
So, sin 0 degrees = y-coordinate of point A = 0.
b. To find cos 0 degrees:
Since 0 degrees lies on the x-axis of the unit circle, the x-coordinate of the point A (1,0) gives us the cosine value.
So, cos 0 degrees = x-coordinate of point A = 1.
c. To find tan 0 degrees:
Since tan 0 degrees is equal to sin 0 degrees divided by cos 0 degrees, we can use the values we found before.
tan 0 degrees = sin 0 degrees / cos 0 degrees = 0 / 1 = 0.
So, sin 0 degrees = 0, cos 0 degrees = 1, and tan 0 degrees = 0.
1. To write the given expressions as functions of an acute angle less than 45 degrees:
a. sin 80: Since 80 degrees is greater than 45 degrees, we need to find the reference angle by subtracting it from 180:
Reference angle = 180 - 80 = 100 degrees
Since sine is positive in the first and second quadrants, and the reference angle is 100 degrees (which is less than 90 degrees), the positive value of the sine function for this angle can be found using a calculator or trigonometric table:
sin 80 = sin 100 degrees
b. sin (-100): Here, we have a negative angle. To find the positive acute angle that is equivalent to -100 degrees, we need to add 360 degrees:
Positive acute angle = -100 + 360 = 260 degrees
Since 260 degrees is greater than 45 degrees, we need to find the reference angle by subtracting it from 360:
Reference angle = 360 - 260 = 100 degrees
Therefore, the positive value of the sine function for this angle is:
sin (-100) = sin 100 degrees
2. To find the trigonometric functions for angle 0, we can use the points A(1,0) and B(0.6,-0.8) on the unit circle O.
a. sin 0: The y-coordinate of point A on the unit circle O is 0. This means that sin 0 is also 0 since sin 0 represents the y-coordinate of a point on the unit circle for angle 0.
b. cos 0: The x-coordinate of point A on the unit circle O is 1. This means that cos 0 is 1 since cos 0 represents the x-coordinate of a point on the unit circle for angle 0.
c. tan 0: To find tan 0, we can use the formula:
tan 0 = sin 0 / cos 0
Since sin 0 is 0 and cos 0 is 1, we get:
tan 0 = 0/1 = 0
Therefore, sin 0 is 0, cos 0 is 1, and tan 0 is 0.
To summarize:
a. sin 0 = 0
b. cos 0 = 1
c. tan 0 = 0
Using the distance formula is not necessary in this case since we already know the coordinates of the points on the unit circle.