evaluate the expression tan (257pi/4)
a.-1
b. -(sqrt2)/2
c. 1
d. (sqrt2)/2
thank you so much, it helps! :)
You're welcome!
To evaluate the expression tan(257π/4), you need to use the trigonometric definition of the tangent function.
The tangent function (tan) is defined as the ratio of the sine (sin) of an angle to the cosine (cos) of the same angle:
tan(x) = sin(x) / cos(x)
In this case, the angle is 257π/4.
First, you need to find the sine and cosine of 257π/4.
The unit circle is commonly used to determine the values of sine and cosine for various angles. In the unit circle, the angle 257π/4 is in the fourth quadrant, and it is equivalent to an angle of π/4.
In the fourth quadrant, the values of sine and cosine are negative.
sin(257π/4) = -sin(π/4) = -(1/√2)
cos(257π/4) = -cos(π/4) = -(1/√2)
Now, divide the sine by the cosine:
tan(257π/4) = -sin(π/4) / -cos(π/4) = (1/√2) / (1/√2) = 1
Therefore, the value of tan(257π/4) is 1.
The correct answer is option c. 1.
tan(x) has a period of π, so
tan(x)=tan(x+π),
in fact,
tan(x+kπ)=tan(x), where k∈Z
So to evaluate
tan(257π/4)
=tan((257/4)π)
=tan(64π + π/4)
=tan(π/4)
I will let you figure out which answer to choose.