### Relating Angle

Relating Angle

Welcome visitors..
In this post, we will explain about Relating Angle. First, the reader must understand the quadrant. From the two-dimensional Cartesian coordinates, we know that there are 4 regions (quadrants) namely on the top right (K I), top left (K II), bottom left (K III) and bottom right (K IV), K stands for quadrant. Consider the following proposition of related angles.

The value of trigonometric ratios (sin, cos, tan, csc, sec and cot) in that quadrant depends on the ratio formula.
For example, the value of tan in quadrant II is $\displaystyle \frac{y(+)}{x(-)}$ or negative (-). Another example, the value of sin in quadrant III is $\displaystyle \frac{y(-)}{r(+)}$ or negative (-). Note that the value of $r$ is always +. The following is a formula for trigonometric ratios for related angles:
$$\text{sin}(90^\text{o}-\alpha)=\text{cos }\alpha$$ $$\text{sin}(270^\text{o}-\alpha)=-\text{cos }\alpha$$ $$\text{cos}(90^\text{o}-\alpha)=\text{sin }\alpha$$ $$\text{cos}(270^\text{o}-\alpha)=-\text{sin }\alpha$$ $$\text{tan}(90^\text{o}-\alpha)=\text{cot }\alpha$$ $$\text{tan}(270^\text{o}-\alpha)=\text{cot }\alpha$$ $$\text{sin}(180^\text{o}-\alpha)=\text{sin }\alpha$$ $$\text{sin}(360^\text{o}-\alpha)=-\text{sin }\alpha$$ $$\text{cos}(180^\text{o}-\alpha)=-\text{cos }\alpha$$ $$\text{cos}(360^\text{o}-\alpha)=\text{cos }\alpha$$ $$\text{tan}(180^\text{o}-\alpha)=-\text{tan }\alpha$$ $$\text{tan}(360^\text{o}-\alpha)=-\text{tan }\alpha$$ $\alpha$ is a special corner. Pay attention to the shape above, every corner of $\displaystyle 90^\text{o}k$, $k$ is odd so it changes (sin becomes cos or vice versa and tan becomes cot or vice versa). For angle $\displaystyle 180^\text{o}n$, $n$ is a natural number so it remains.
Example:
sin (150$\displaystyle ^\text{o}$) = ....
Solution:
$$=\text{sin}(180-30)^\text{o}$$ $$=\text{sin }30^\text{o}=\frac{1}{2}$$
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