. Given sec θ = 13/12, calculate all other trigonometric ratios.
Answers
Answered by
10
SOLUTION
Let ΔABC be a right-angled triangle, right-angled at B. We know that sec θ = OP/OM = 13/12 (Given) Let OP be 13k and OM will be 12k where k is a positive real number. By Pythagoras theorem we get, OP2 = OM2 + MP2 (13k)2 = (12k)2 + MP2 169k2 - 144k2 = MP2 MP2 = 25k2 MP = 5 Now, sin θ = MP/OP = 5k/13k = 5/13 cos θ = OM/OP = 12k/13k = 12/13 tan θ = MP/OM = 5k/12k = 5/12 cot θ = OM/MP = 12k/5k = 12/5 cosec θ = OP/MP = 13k/5k = 13/5
Let ΔABC be a right-angled triangle, right-angled at B. We know that sec θ = OP/OM = 13/12 (Given) Let OP be 13k and OM will be 12k where k is a positive real number. By Pythagoras theorem we get, OP2 = OM2 + MP2 (13k)2 = (12k)2 + MP2 169k2 - 144k2 = MP2 MP2 = 25k2 MP = 5 Now, sin θ = MP/OP = 5k/13k = 5/13 cos θ = OM/OP = 12k/13k = 12/13 tan θ = MP/OM = 5k/12k = 5/12 cot θ = OM/MP = 12k/5k = 12/5 cosec θ = OP/MP = 13k/5k = 13/5
Answered by
6
sin thita= 5/12
cos thita=12/13
tan thita=5/12
cosec thita=12/5
cot thita=12/5
cos thita=12/13
tan thita=5/12
cosec thita=12/5
cot thita=12/5
Similar questions