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Trigonometry is an important topic for your higher studies. We must study this topic with all basics. Actually, this topic is very simple. If we concentrate to learn this topic from the beginning, we will definitely understand the basics of this topic and it will help us to remember the formulas (formulae) very easily. At the end of all the Blogs related to “Basics of trigonometry”, we will list all the formulas (formulae) in a separate sheet so that it will be helpful for you to remember all these formulas (formulae).
1) Define all trigonometric ratios for an angle C of the above triangle ABC.
Answer:
1) sin C = AB/AC
2) cos C = BC/AC
3) tan C = AB/BC
4) csc C = AC/AB
5) sec C = AC/BC
6) cot C = BC/AB
2) Observe the adjacent figure and write down all the trigonometric ratios.
Answer:
1) sin P = RQ/PQ 1) sin Q = PR/PQ
2) cos P = PR/PQ 2) cos Q = RQ/PQ
3) tan P = RQ/PR 3) tan Q = PR/RQ
4) csc P = PQ/RQ 4) csc Q = PQ/PR
5) sec P = PQ/PR 5) sec Q = PQ/RQ
6) cot P = PR/RQ 6) cot Q = RQ/PR
In the above example, just observe
case 1) sin P and cos Q
case 2) cos P and sin Q
Here, the basic point to understand is that the comparison of two angles is given with different trigonometric ratios. First, observe these two angles. angle P and angle Q. In a rightangled triangle, QPR, Angle R = 90, so the remaining two angles P and Q are complementary angles.
Here all of us will remember the following trigonometric relations of complementary angles of a rightangled triangle.
Here all of us will remember the following trigonometric relations of complementary angles of a rightangled triangle.
1) sin A = cos (90A)
2) cos A = sin (90A)
3) sec A = csc (90A)
4) csc A = sec (90A)
5) tan A = cot (90A)
6) cot A = tan (90A)
A) An easy way to remember the above relations:
The relation between the trigonometric ratios of coterminal angles. (See the following figure)
Trigonometric Ratios of Complimentary Angle of A. (90°A)

Ratio (In the form of the length of the sides of a triangle)
 
sin A

cos (90°A)

BC/AC

cos A

sin (90°A)

AB/AC

csc A

sec (90°A)

AC/BC

sec A

csc (90°A)

AC/AB

tan A

cot (90°A)

BC/AB

cot A

tan (90°A)

AB/BC

B) Relation between the trigonometric ratios:
Observe the following trigonometric ratios from the figure given below:
2) cos C = BC/AC
3) tan C = AB/BC
4) csc C = AC/AB
5) sec C = AC/BC
6) cot C = BC/AB
If we divide equation 1 by equation 2 we get equation 3. i.e.
In the same way, we can prove that "cos C / sin C = cot C"
In the Next Blog, we will study the trigonometric ratios of some standard angles and trigonometric identities.