In ΔABC, right-angled at B, AB = 24 cm, BC = 7 cm. Determine:
(i) sin A, cos A
(ii) sin C, cos C
(i) sin A = \(\frac{7}{25}\), cos A = \(\frac{24}{25}\)
(ii) sin C = \(\frac{24}{25}\), cos C = \(\frac{7}{25}\)
In Fig. 8.13, find tan P − cot R.
0
If sin A = \(\frac{3}{4}\), calculate cos A and tan A.
cos A = \(\frac{\sqrt{7}}{4}\), tan A = \(\frac{3}{\sqrt{7}}\)
Given 15 cot A = 8, find sin A and sec A.
sin A = \(\frac{15}{17}\), sec A = \(\frac{17}{8}\)
Given sec θ = \(\frac{13}{12}\), calculate all other trigonometric ratios.
sin θ = \(\frac{5}{13}\), cos θ = \(\frac{12}{13}\), tan θ = \(\frac{5}{12}\), cot θ = \(\frac{12}{5}\), cosec θ = \(\frac{13}{5}\)
If ∠A and ∠B are acute angles such that cos A = cos B, then show that ∠A = ∠B.
If cot θ = \(\frac{7}{8}\), evaluate:
(i) \(\frac{(1 + \sin θ)(1 - \sin θ)}{(1 + \cos θ)(1 - \cos θ)}\)
(ii) cot² θ
(i) \(\frac{49}{64}\)
(ii) \(\frac{49}{64}\)
If 3 cot A = 4, check whether \(\frac{1 - \tan^2 A}{1 + \tan^2 A} = \cos^2 A - \sin^2 A\) or not.
Yes
In triangle ABC, right-angled at B, if tan A = \(\frac{1}{\sqrt{3}}\), find:
(i) sin A cos C + cos A sin C
(ii) cos A cos C − sin A sin C
(i) 1
(ii) 0
In ΔPQR, right-angled at Q, PR + QR = 25 cm and PQ = 5 cm. Determine sin P, cos P and tan P.
sin P = \(\frac{12}{13}\)
cos P = \(\frac{5}{13}\)
tan P = \(\frac{12}{5}\)
State whether the following are true or false. Justify your answer:
(i) The value of tan A is always less than 1.
(ii) sec A = \(\frac{12}{5}\) for some value of angle A.
(iii) cos A is the abbreviation used for the cosecant of angle A.
(iv) cot A is the product of cot and A.
(v) sin θ = \(\frac{4}{3}\) for some angle θ.
(i) False
(ii) True
(iii) False
(iv) False
(v) False