Functions of Large and Negative Angles
![](/math/trigonometry/images/functions_of_large_and_negative_angles_2.png)
This leads to the functions being positive in the following quadrants.
![](/math/trigonometry/images/functions_of_large_and_negative_angles_1.png)
Let's look at an example of a large angle. Consider the following graph of a 200° angle. A right triangle is created using the x axis and the terminal side of the angle.
![](/math/trigonometry/images/functions_of_large_and_negative_angles_3.jpg)
![](/math/trigonometry/images/functions_of_large_and_negative_angles_5.png)
![](/math/trigonometry/images/functions_of_large_and_negative_angles_6.png)
Let's look at an example of a negative angle. Consider the graph of a -31° angle. A right triangle is created using the x axis and the terminal side of the angle.
![](/math/trigonometry/images/functions_of_large_and_negative_angles_4.jpg)
![](/math/trigonometry/images/functions_of_large_and_negative_angles_7.png)
![](/math/trigonometry/images/functions_of_large_and_negative_angles_8.png)
Notice that the sine ratio still holds true with only a variance in sign based on the quadrant in which the terminal side of the angle lies. The same will also apply to the other trig ratios: cosine, tangent, secant, cosecant and cotangent.
Related Links: Math Trigonometry Inverse Trigonometric Functions Quadrantal Angles |
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