find the exact values of the six trig functions of angle...
sin(-315degrees)
how do i do this?
sin(-315)=sin(-315+360)=sin(45)=sqrt(2)/2
To find the exact values of the six trigonometric functions of an angle, including sin(-315 degrees), you can follow these steps:
Step 1: Determine the reference angle:
The reference angle is the positive acute angle formed between the terminal side of the angle and the x-axis. To find the reference angle for -315 degrees, you can add 360 degrees to it repeatedly until you get a positive angle between 0 and 360 degrees.
-315 degrees + 360 degrees = 45 degrees
So, the reference angle is 45 degrees.
Step 2: Determine the quadrant:
Based on the given angle, -315 degrees, it lies in the fourth quadrant where both the x and y coordinates are negative.
Step 3: Evaluate the trigonometric functions:
Since the sine function is positive in the fourth quadrant, use the reference angle of 45 degrees to determine the sign of the trigonometric functions:
sin(-315 degrees) = -sin(45 degrees)
Now, you can use the trigonometric values of the reference angle (45 degrees) to evaluate the sine function:
sin(45 degrees) = √2 / 2
Therefore, the exact value of sin(-315 degrees) is -√2 / 2.
Note: For the remaining trigonometric functions, you can use the reciprocal and quotient identities or the unit circle to determine their values.