If tan theta= 1/5
Simplify tan(540-theta)
In the unit circle do I have to go clockwise or anti-clockwise from the fourth quadrant?
Please help is needed for this
Since 540 = 3*180
and the period of tan(x) is 180
tan(540-x) = tan(-x) = -tan(x) = -1/5
However, to answer your question, yo need to go clockwise, since you have tan(-x).
To simplify the expression tan(540 - θ), you can use the trigonometric identity:
tan(540 - θ) = -tan(θ)
To determine whether you need to go clockwise or counterclockwise from the fourth quadrant on the unit circle, let's first understand the angles involved.
In the unit circle, the fourth quadrant falls in the range of 270 to 360 degrees (or π/2 to 2π).
For tan θ = 1/5, we can find the reference angle (θ) by calculating the inverse tangent (arctan) of 1/5:
θ = arctan(1/5) ≈ 11.31 degrees
Now, let's determine the value of tan(540 - θ):
tan(540 - θ) = -tan(θ) = -(1/5)
So, the simplified expression is -1/5.
To answer your second question, when working with angles on the unit circle, you generally move counterclockwise from the positive x-axis. However, in this case, we're not using the unit circle to find the value of tan(540 - θ). Instead, we're using the trigonometric identity mentioned above.
To simplify tan(540 - theta), we can use the following identity:
tan(540 - theta) = -tan(theta)
Since tan(theta) is given as 1/5, we can substitute it into the above identity:
tan(540 - theta) = -1/5
As for the direction in the unit circle, the fourth quadrant is located in the lower right portion of the circle. When moving from the fourth to the third quadrant, you have to go clockwise, which means the angle theta would decrease as you traverse from the fourth to the third quadrant.
I hope this helps! Let me know if you have any other questions.