Find ratio of Sin, Cosec, Cos, Sec, Tan and Cot - Trigonometry : Solved Examples

T Ratios of Angles - 30, 45, 60 & 90 degree angles

Find Height, Distance using T - Ratios

If Cot Θ = 3/5, find Cosec Θ and Sec Θ Lets draw the right angle triangle with the above mentioned details Given thing are Cot Θ = 3/5 we know that Cot Θ = Adjacent Side / Opposite Side, so we get Opposite Side = 3 Adjacent Side = 5 Hypotenuse : BC = ? Adjacent Side : AB = 5 (Adjacent to ∠ Θ) Opposite Side : AC = 3 (Opposite to ∠ Θ) To find the Hypotenuse : BC , we use Pythagoras theorem ((Hypotenuse)2 = (Leg 1)2 + (Leg 2)2)   __________ BC = √  AB2 + AC2    _______ BC = √  52 + 32    _______ BC = √  25 + 9    __ BC = √  34  Now we will try to simplify square root of 34. As no pairs can be made the final value will be   __ BC = √  34  So Cosec, Sec and Cot will be as follows - Cosec Θ = Hypotenuse / Opposite Side   ___ Cosec Θ = √  34  / 3 Sec Θ = Hypotenuse / Adjacent Side   ___ Sec Θ = √  34  / 5 Cot Θ = Adjacent Side / Opposite Side Cot Θ = 5 / 3 Related Question Examples △ ABC is right angle triangle at B, AB=8, BC=11, AC=13. Write sin C, cos A, tan C △ PQR is right angle triangle at P, PQ=9, QR=11, RP=7. Write sin Q, cos R, tan Q △ ABC is right angle triangle at A, AB=11, BC=13, AC=8. Write sin A, cos C, tan A △ PQR is right angle triangle at Q, PQ=7, QR=9, PR=11. Write sin R, cos R, tan P △ ABC is right angle triangle at B, AB=11, BC=9, AC=17. Write sin A, cos C, tan C △ PQR is right angle triangle at Q, PQ=13, QR=7, PR=19. Write sin R, cos P, tan P If cos Θ = 11/13, find sin Θ and tan Θ If sin Θ = 7/11, find cos Θ and tan Θ If cos Theta = 2/3, find sin and tan theta If Tan Θ = 3/5, find sin Θ and cos Θ △ ABC is right angle triangle at B, AB=8, BC=11, AC=13. Write Cosec C, Sec A, Cot C If Sin Θ = 5/7, find cos Θ and tan Θ If Tan Θ = 2/3, find Sin Θ and Cos Θ △ ABC is right angle triangle at A, AB=11, BC=13, AC=8. Write Cosec A, Sec C, Cot A △ PQR is right angle triangle at P, PQ=9, QR=11, RP=7. Write Cosec Q, Sec R, Cot Q △ PQR is right angle triangle at Q, PQ=7, QR=9, PR=11. Write Cosec R, Sec R, Cot P △ ABC is right angle triangle at B, AB=11, BC=9, AC=17. Write Cosec A, Sec C, Cot C △ PQR is right angle triangle at Q, PQ=13, QR=7, PR=19. Write Cosec R, Sec P, Cot P If Sec Θ = 11/13, find Cosec Θ and Cot Θ If Cosec Θ = 7/11, find Sec Θ and Cot Θ If Cot Θ = 3/5, find Cosec Θ and Sec Θ If Sec Θ = 2/3, find Cosec Θ and Cot Θ If Cosec Θ = 5/7, find Sec Θ and Cot Θ If Cot Θ = 2/3, find Cosec Θ and Sec Θ