1) use the half-angle formulas to determine the exact values of the sine, cosine, and tangent of the angle.
67 degrees and 30'
Please explain!! I do not know how to start.
http://www.jiskha.com/display.cgi?id=1267478813
To use the half-angle formulas to determine the exact values of the sine, cosine, and tangent of the angle, you can follow these steps:
1. Convert the angle measure to radians. Since the given angle is in degrees and minutes, we need to convert it to decimal degrees first. The conversion formula is: decimal degrees = degrees + (minutes / 60). Let's perform the conversion for the given angle:
Degrees = 67
Minutes = 30
Decimal degrees = 67 + (30 / 60) = 67.5 degrees
Now, we need to convert the decimal degrees to radians. The conversion formula is: radians = (pi / 180) * degrees.
Radians = (pi / 180) * 67.5
2. Apply the half-angle formulas to find the exact values of sine, cosine, and tangent. The half-angle formulas are:
sin(x/2) = sqrt((1 - cos(x)) / 2)
cos(x/2) = sqrt((1 + cos(x)) / 2)
tan(x/2) = sin(x) / (1 + cos(x))
Let's substitute the angle converted to radians into the formulas:
sin(67.5/2) = sqrt((1 - cos(67.5)) / 2)
cos(67.5/2) = sqrt((1 + cos(67.5)) / 2)
tan(67.5/2) = sin(67.5) / (1 + cos(67.5))
3. Use a calculator or mathematical software to compute the exact values. Substitute the cosine value for the given angle into the formulas and calculate the values of sine, cosine, and tangent.
sin(67.5/2) = sqrt((1 - cos(67.5)) / 2)
cos(67.5/2) = sqrt((1 + cos(67.5)) / 2)
tan(67.5/2) = sin(67.5) / (1 + cos(67.5))
Plug in the appropriate values into your calculator or use mathematical software to evaluate these expressions. The resulting values will be the exact values of sine, cosine, and tangent for the given angle.
I hope this explanation helps! Let me know if you have any further questions.