\
sec(3π/4)
The image provided shows the trigonometric expression sec(3π/4). To solve this, we must determine the exact numerical value of the secant of the angle 3π/4 radians.
The secant function, abbreviated as sec, is one of the six fundamental trigonometric functions. It is defined as the reciprocal of the cosine function. This relationship can be written as the identity: sec(x) = 1/cos(x). Using this identity, we can rephrase our problem from√2 / 2.
The final step is to simplify the expression by canceling the common factor of 2 from the numerator and the denominator, which leaves us with -√2. finding sec(3π/4) to finding 1/cos(3π/4). Our first step, therefore, is to evaluate cos(3π/4).
To find the value of cos(3π/4), we can visualize the angle on the unit circle. The angle 3π/4 radians is equivalent to 135 degrees. This places the angle in the second quadrant of the Cartesian coordinate system, as it lies between π/2 (90°) and π (180°). On the unit circle, the cosine of an angle corresponds to the x-coordinate of the point where the terminal side of the angle intersects the circle. In the second quadrant, all x-coordinates are negative, which means the value of cos(3π/4) will be negative.
Next, we find the reference angle, which is the acute angle that the terminal side of 3π/4 makes with the horizontal x-axis. For an angle in the second quadrant, the reference angle is calculated as π minus the angle. So, the reference angle is π – 3πthumb_upthumb_down
30.7s
The Correct Answer and Explanation is: