PROBLEMS ON TRIGONOMETRIC RATIOS

About "Problems on trigonometric ratios"

Problems on trigonometric ratios are much useful to the students who would like to practice problems on Trigonometry.

Before, we look at the problems on trigonometric ratios, we have to be clear with SOHCAHTOA.

SOHCAHTOA is the shortcut to remember the trigonometric ratios sin, cos and tan. 

Let us see, how this shortcut works to remember the above mentioned trigonometric ratios. 

Before we discuss this shortcut, let us know the name of each side of a right triangle from the figure given below.  

To understand the shortcut, first we have to divide SOHCAHTOA in to three parts as given below. 

What do SOH, CAH and TOA stand for ?

Here is the answer

From the above figures, we can derive formulas for the three trigonometric ratios sin, cos and tan as given below. 

Reciprocal Relations

The trigonometric ratios csc θ, sec θ and cot θ are the reciprocals of sin θ, cos θ and tan θ respectively.

Problems on trigonometric ratios

Problem 1 :

In the right triangle PQR given below, find the six trigonometric ratios of the angle θ

Solution :

From the figure given above,

opposite side  =  5

adjacent side  =  12

hypotenuse  =  13

Therefore,

Problem 2 :

From the figure given below, find the six trigonometric ratios of the angle θ.

Solution : 

From the figure given above, AC = 24 and BC = 7.

By Pythagorean theorem, 

AB²  =  BC² + CA²  

AB²  =  7² + 24²

AB²  =  49 + 576

AB²  =  625

AB²  =  25²

AB  =  25 

Now, we can use the three sides find the six trigonometric ratios of angle θ.

Therefore, 

Problem 3 :

In triangle ABC, right angled at B, 15 sin A = 12. Find the other five trigonometric ratios of the angle A. Also find the six ratios of the angle C

Solution : 

Given that 15 sin A = 12,  so sin A = 12 / 15

Therefore, opposite side  =  12 and hypotenuse  =  15

Let us consider the triangle ABC where right angled at B, with     BC  =  12 and AC  =  15.  

By Pythagorean theorem, 

AC²  =  AB² + BC²  

15²  =  AB² + 12²

AB²  =  15² - 12²

AB²  =  225 - 144

AB²  =  81

AB²  =  9²

AB  =  9 

Now, we can use the three sides find the five trigonometric ratios of angle A and six trigonometric ratios of angle C.

Therefore, 

After having gone through the stuff given above, we hope that the students would have understood "Problems on trigonometric-ratios"

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