Question

If tan θ= 15/8, find the value of all T-ratios of θ

Answer 1

ANSWER:

sinθ= 15/17

Cosecθ= 17/15

tanθ=15/8

cotθ= 8/15

Cosθ= 8/17

secθ= 17/8

GIVEN:

tanθ=15/8

TO FIND:

Value of all trigonometric ratios of θ

SOLUTION:

Fomula:

1+tan²θ=sec²θ

Putting tanθ=15/8

=> 1+(15/8)² = sec²θ

=> 1+225/64 = sec²θ

=> (64+225)/64 = sec²θ

=> 289/64 = sec²θ

=> secθ=√289/√64

=> secθ= 17/8

=> cosθ= = 1/secθ

=> Cosθ= 8/17

=> Cotθ= 1/tanθ

=> cotθ= 8/15

Formula:

=> Sin²θ+cos²θ= 1

Putting Cosθ=8/17 we get:

=> Sin²θ=1-(8/17)²

=> sin²θ= 1-64/289

=> sin²θ= (289-64)/289

=> sin²θ= 225/289

=> sinθ= √225/√289

=> sinθ= 15/17

=> Cosecθ= 1/sinθ

=> Cosecθ= 17/15

Answer 2

Referred to the attachments......