Find the exact values of the cosine and sine of the angle. Then find the decimal values. Show your work step by step.
0 = 315°
To find the exact values of the cosine and sine of the angle, we will use the unit circle.
Step 1: Convert the angle from degrees to radians.
To convert from degrees to radians, we use the formula: radians = (degrees × π) / 180
For 315°, the radians would be:
radians = (315 × π) / 180 = (7π/4) radians
Step 2: Look at the unit circle and find the point corresponding to (7π/4) radians.
The point on the unit circle that corresponds to (7π/4) radians is located at the angle (135° on the unit circle).
Step 3: Find the cosine and sine values of the angle.
The cosine value is given by the x-coordinate of the point on the unit circle, and the sine value is given by the y-coordinate of the point.
For the angle 135°, the cosine and sine values are:
cos(135°) = -√2/2
sin(135°) = √2/2
Step 4: Convert the exact values to decimal values.
Using a calculator, we can find the decimal values:
cos(135°) ≈ -0.707
sin(135°) ≈ 0.707
Therefore, the exact values of the cosine and sine of the angle 0 = 315° are:
cos(315°) = -√2/2
sin(315°) = √2/2
The decimal values of the cosine and sine of the angle 0 = 315° are approximately:
cos(315°) ≈ -0.707
sin(315°) ≈ 0.707