1. In each of the following, one of the six trigonometric ratios s given. Find the values of the other trigonometric ratios.
(i) sin A = 2/3
(ii) cos A = 4/5
(iii) tan θ = 11/1
(iv) sin θ = 11/15
(v) tan α = 5/12
(vi) sin θ = √3/2
(vii) cos θ = 7/25
(viii) tan θ = 8/15
(ix) cot θ = 12/5
(x) sec θ = 13/5
2. In a △ ABC, right angled at B, AB = 24 cm , BC = 7 cm. Determine
(i) sin A , cos A (ii) sin C, cos C
3. In fig. 5.37, find tan P and cot R. Is tan P = cot R?
4. If sin A = 9/41, compute cos A and tan A.
5. Given 15cot A= 8, find sin A and sec A.
6. In △PQR, right-angled at Q, PQ = 4cm and RQ = 3 cm. Find the value of sin P, sin R, sec P and sec R.
7. If cot θ = 7/8, evaluate
(i) (1+sin θ)(1–sin θ)/ (1+cos θ)(1–cos θ)
(ii) cot2 θ
8. If 3cot A = 4, check whether (1–tan2A)/(1+tan2A) = (cos2A – sin2A) or not.
9. If tan θ = a/b, find the value of (cos θ + sin θ)/ (cos θ – sin θ)
10. If cos θ = 12/13, show that sin θ(1 – tan θ) = 35/156