Question

In each of the following, one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios.
(i) sinA = 2/3 (ii) cos A =4/5
(iii) tan ⁡θ = 11 (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) cos⁡θ = 12/5 (x) sec ⁡θ = 13/5
(xi) cosec⁡θ =√10 (xii) cos⁡θ = 12/15

Answer 1

Step-by-step explanation:

hope it helps you follow me....

Answer 2

Trigonometric ratios

Step-by-step explanation:

(i) Given (i) sinA = 2/3  

sin A = 2/3 = opposite side / hypotenuse

So adjacent side = √(3² - 2²) = √(9-4) = √5

The other trigonometri values are:

Cos A = Adjacent / hypotenuse = √5/3

Tan A = Sin A/ CosA = 2/3 / √5/3 = 2 /√5

Cosec A = 1/ SinA = 3/2

Sec A = 1/ Cos A = 3/√5

Cot A = 1/Tan A = √5 / 2

(ii) cos A = 4/5  

 Cos A = 4/5 = Adjacent / hypotenuse

So opposite side = √(5² - 4²) = √(25-16) = √9 = 3

The other trigonometri values are:

Sin A = opposite / hypotenuse = 3/5

Tan A = Sin A/ CosA = 3/5 / 4/5 = 3/4

Cosec A = 1/ SinA = 5/3

Sec A = 1/ Cos A = 5/4

Cot A = 1/Tan A = 4/3

Solve the rest of the question in the same method.