 # CHANGE OF TRIGONOMETRIC RATIOS WITH TRIGONOMETRIC ANGLE

Till now we have seen Trigonometric Ratios for Right angle Triangle w.r.t. angle \theta . What will happen, if we change the Trigonometric angle to (90 -\theta ) angle? Lets see.

But before that, lets have some more clarity over Trigonometric Ratios for a Right angle Triangle. Let’s see in more detail.

AC is PERPENDICULAR for the \triangle ABC w.r.t. angle \theta .

AB is BASE for the \triangle ABC w.r.t. angle \theta .

BC is HYPOTENUSE for the \triangle ABC w.r.t. angle \theta .

Here all these Trigonometric sides are w.r.t. angle \theta . Based on these Trigonometric Sides, we got our Trigonometric Ratios as ## Change of Trigonometric Angle

In above case, all things are w.r.t. angle \theta . Now, what will happen, if we change Trigonometric angle from \theta to 90-\theta . Now, we will determine the Trigonometric sides as per new Trigonometric angle i.e. 90-\theta .

AB is PERPENDICULAR for the \triangle ABC with respect to angle 90-\theta . [Why? Comment Below]

AC is BASE for the \triangle ABC with respect to angle 90-\theta . [Why? Comment Below]

BC is HYPOTENUSE for the \triangle ABC with respect to angle 90-\theta .

All these sides are with respect to Trigonometric angle 90-\theta . ### Changed Trigonometric Ratios

Based on these new Trigonometric Sides, we got our Trigonometric Ratio’s as We got Trigonometric ratios for \theta and 90-\theta angle. Lets compare both the Trigonometric Ratios. On comparing, we got a new set of formulas. These formulas, involving relation between Trigonometric ratios, will be useful in solving many Trigonometric questions, that we will see in future posts.

In previous post also, we have seen relation between Trigonometric ratios. Note these formula, with the formulas in previous posts.

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