If tan θ= 15/8, find the value of all T-ratios of θ
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Answered by
1
Answer:sinθ=15/17
cosθ= 8/17
cosecθ= 17/15
cotθ=8/15
secθ=17/8
Step-by-step explanation:
tanθ=15/8
b=8,p=15,h=?
h²=b²+p²
h²=8²+15²
h²=64+225
h²=289
h=17
sinθ=15/17
cosθ= 8/17
cosecθ= 17/15
cotθ=8/15
secθ=17/8
Answered by
12
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
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