Introduction To Trigonometry

Important Formula (Trigonometry class ten) and Chapter Summary

In the right angle triangle ABC, the right angle is ∠ B.     The value of sin or cos never exceeds 1, but the value of sec and cosec is always greater than or equal to 1. Exercise 8.1

Question 1 - In triangle ABC, right-angled at B, AB = 24 cm, BC = 7 cm. Determine: (a) Sin A, Cos A

Solution: AB = 24 cm, BC = 7 cm, AC = ?

The value of AC can be calculated by using Pythagoras Theorem: (b) Sin C, Cos C

Solution: Question 2 - In the given figure, find tan P cot R. Solution: Value of QR can be calculated by using Pythagoras theorem: Now; Question 3 - If sin A = , calculate cos A and tan A.

Solution: Sin A = = p/h

We can calculate b by using Pythagoras theorem; Now; Question 4 - Given 15 cot A = 8, find sin A and sec A.

Solution: 15 cot A = 8 This means, b = 8 and p = 15

We can calculate h by using Pythagoras theorem; Now; Question 5 - Given sec θ = 13/12, calculate all other trigonometric ratios.

Solution: This means, h = 13 and b = 12.

We can calculate p by using Pythagoras theorem; Other trigonometric ratios can be calculated as follows: Question 6 - If ∠ A and ∠ B are acute angles such that cos A = cos B, then show that ∠ A = ∠ B

Solution: For no two different angles the cos ratio is same. (Ref: Table of trigonometric ratio).

Question 7 - If cot θ = 7/8, evaluate:

Solution: This means, b = 7 and p = 8.

We can calculate h by using Pythagoras theorem;  Solution: Solution: Question 8 - If 3 cot A = 4, check whether or not.

Solution: 3 cot A = 4 means cot A = 4/3 = b/p

Hence, p = 3 and b = 4.

We can calculate h by using Pythagoras theorem; Now; the equation can be checked as follows:

LHS: RHS: It is clear that LHS = RHS.

Question 9 - In triangle ABC, right-angled at B, if tan A = find the value of:

Solution:  We can calculate h by using Pythagoras theorem; (a) Sin A Cos C + Cos A Sin C

Solution:

Sin A Cos C + Cos A Sin C (b) Cos A Cos C Sin A Sin C

Solution:

Cos A Cos C Sin A Sin C Question 10 - In triangle PQR, right-angled at Q, PR + QR = 25 cm and PQ = 5 cm. Determine the values of sin P, cos P and tan P. Solution: Given; PR + QR = 25 cm and PQ = 5 cm.

Hence, PR = 25 QR

We can calculate PR and QR by using Pythagoras theorem; Now; Question 11 - State whether the following are true or false. Justify your answer.

(a) The value of tan A is always less than 1.

Solution: False; value of tan begins from zero and goes on to become more than 1.

(b) sec A = 12/5 for some value of angle A.

Solution: True, value of cos is always more than 1.

(c) cos A is the abbreviation used for the cosecant of angle A.

Solution: False, cos is the abbreviation of cosine.

(d) cot A is the product of cot and A.

Solution: False, cot A means cotangent of angle A.

(e) sin A = 4/3 for some angle A.

Solution: False, value of sin is less than or equal to 1, while this value is more than 1.

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