how does tan 110 equal tan290
actually, 180° is 1/2 rotation around the circle.
But tanx has a period of π, which is why the two are equal.
To understand why tan 110° is equal to tan 290°, we need to remember that the tangent function is periodic with a period of 180°. This means that the value of the tangent function repeats every 180°.
Let's use the fact that the tangent function has a periodicity of 180° to find the relationship between tan 110° and tan 290°.
Step 1: Identify the related angle.
Since tan 290° is beyond one complete revolution (360°), we can find the related angle by subtracting 360° from 290°.
Related angle = 290° - 360° = -70°
Step 2: Use the periodicity of the tangent function.
The tangent function has a periodicity of 180°. This means that the tangent of an angle and its related angle have the same value.
tan 110° = tan (-70°)
Step 3: Calculate the value of the tangent.
Now we can evaluate the tangent function for both angles using a calculator or a table:
tan 110° ≈ 1.9648
tan (-70°) ≈ 1.9648
Therefore, tan 110° is equal to tan 290°, as both angles have the same tangent value of approximately 1.9648.
The trigonometric functions such as tangent (tan) are periodic, which means they repeat their values after a certain interval. In the case of the tangent function, it has a period of 180 degrees or π radians. This means that the values of tan(θ) and tan(θ + 180°) are equal.
In the given question, tan(110°) and tan(290°) are being compared. To understand their relationship, it is helpful to find an equivalent angle within the range of 0° to 180°.
We can subtract multiples of 180° from 290° to bring it within the range of 0° to 180°:
290° - 180° = 110°
Now, we can see that 290° is equivalent to 110° within that range. Therefore, tan(110°) and tan(290°) are equal.
So, to calculate tan(110°), you can directly use a calculator or a trigonometric table, or you can use the relationship between 290° and 110° to simplify the calculation.
Note: Make sure your calculator is set to degrees (°) mode.
110x(π/180)= 0.611π
290x(π/180)= 1.611π
1.611π-0.611π= 1
If difference is one, than it is one rotation around the circle
Dont forget about your unit circle