Trigonometry is the 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 of all the formulas (formulae) in the separate sheet so that it will be helpful for you to remember all these formulas (formulae).
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 above example, just observe
case 1) sin P and cos Q
case 2) cos P and sin Q
1) sin C = AB/AC
In the same way, we can prove that
In Blog82, we asked the following two questions. We are sure that you might get the answers to these questions. We will see both the answers one by one.
1) Define all trigonometric ratios for an angle C of 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 above example, just observe
case 1) sin P and cos Q
case 2) cos P and sin Q
Here, basic point to understand is this 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 remaining two angles P and Q are complementary angles.
Here all of us will remember 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)
B) Relation between the trigonometric ratios:
Observe the following trigonometric ratios from the figure given bellow:
Here all of us will remember 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 bellow:
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
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.
Anil Satpute
In the Next Blog, we will study the trigonometric ratios of some standard angles and trigonometric identities.
Anil Satpute