For value cos (8ð/3).
b) write cos (8ð/3) in terms of an algebraic sign and cosine of the reference angle
find the exact value of what you found in part b using a cheating chart. no decimals please
The reference angle for 8pi/3 is pi/3.
8pi/3 = 6pi/3 + 2pi/3
= 2pi+2pi/3
2pi/3 is in the second quadrant, where cosine is negative and cos(pi/3)=1/2
So the cos(8pi/3)= -cos(pi/3) = -1/2
so what is the exact value of what you found in part b using a cheating chart. no decimals please??
-1/2
how about when i draw an angle in standard position. and label and find the value of the reference angle.
When you draw the angle in standard position, the ray will be in the second quadrant. Draw a line segment from the end of the ray down to the x-axis to make a triangle. The reference angle is pi/3. Along the horizontal part of the triangle write -1/2. Along the vertical part of the triangle, write sqrt(3)/2, Label the hypotenuse as 1. Cosine = the adjacent side/the hypotenuse, right? So that's (-1/2)/1 = -1/2 Are you supposed to prove how you know that sqrt(3)/2 and -1/2 are the side lengths of the triangle? I can explain that too if you want.
You may want to look up "unit circle" on google. There's an excellent picture with all the angles and their measures labeled.
To write cos (8ð/3) in terms of an algebraic sign and cosine of the reference angle, we need to determine the reference angle for the given angle.
The reference angle is the positive acute angle between the terminal side of the angle and the x-axis in standard position.
To find the reference angle, we subtract the given angle from the nearest multiple of 2ð (360 degrees) that is greater than the given angle.
In this case, the nearest multiple is 2ð, so we subtract (8ð/3) from (2ð):
Reference angle = (2ð) - (8ð/3)
= (6ð/3) - (8ð/3)
= -2ð/3
Since the given angle is negative, the algebraic sign will be negative. Therefore,
cos (8ð/3) = -cos (-2ð/3)
Now, to find the exact value using a "cheating chart" or reference chart, we need to determine the value of cosine for the reference angle (-2ð/3).
Note: The reference chart is a table that lists the exact values of the trigonometric functions for certain common angles, such as 0°, 30°, 45°, 60°, and 90°.
Looking at the reference chart, we find that the exact value of cosine for -2ð/3 is -1/2.
Therefore, the exact value of -cos(-2ð/3) is -(-1/2), which simplifies to 1/2.