if tan theta =15/8 find the value of all T-ratioes of theta
Answers
Answer:
Hey there!
We know that,
tanθ = Opposite side to theta / Adjacent side to theta
tanθ = 15/8
Adjacent side = 8
Opposite side = 15
By Pythagoras theorem,
( Hypotenuse )² = (Adjacent side) ²+ (Opposite side)²
Hypotenuse =√ ( 8² + 15² ) = √ 64 + 225 = √289 = 17
Now, Trigonometry ratios :
cosθ = Adjacent side to theta / Hypotenuse = 8/17
sinθ = Opposite side of theta / Hypotenuse = 15/17
cotθ = 1/tanθ = 1/(15/8) = 8/15
secθ = 1/cosθ = 1/(8/17) = 17/8
cscθ = 1/sinθ = 1/(15/17) = 17/15
∴ The trigonometric ratios , cosθ = 8/17 , sinθ = 15/17 , cotθ = 8/15 , secθ = 17/8 , cosecθ = 17/15
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Step-by-step explanation:
tan theta=15/8
P/B=15/8
by pyhagoras theorem
Psquare= Bsquare+Hsquare
15×15=8×8+Hsquare
225=64+Hsquare
225-64=Hsquare
161=Hsquare
underroot161=H
12.7=H
sintheta=15/12.7
costheta=8/12.8
cosectheta=12.8/15
sectheta=12.8/8
cottheta=8/15