Question

tan = -2 ,lies in second quardrant, find the values of other five trigonometric functions

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Answer 1

tan∅ = -2

we know,

>cot∅ = 1/tan∅ = 1/-2 = -1/2

>1+tan²∅ = sec²∅

=>1+(-2)² = sec²∅

=>1+4 = sec²∅

=>5 = sec²∅

=>sec∅ = √5

we know,

cos∅ = 1/sec∅ = 1/√5 = √5/5

now,

we know

sin²∅ = 1-cos²∅

=>sin²∅ = 1-(1/√5)² = (1-1/5) = 4/5

=>sin∅ = 2/√5 = 2√5/5

we know,

cosec∅ = 1/sin∅ = 1/2/√5 = √5/2

quick recap:-

if tan∅ = -2

then,

cot∅ = -1/2

sec∅ = -√5

cos∅ =- 1/√5

sin∅ = 2/√5

cosec∅ = √5/2

{ps:- In the second quadrant only cosec and sin are positive}

Cheers!