Question: Given 15 cot A = 8, find sin A and sec A
In problems like these, make sure you know all the formulas mentioned in the notes basics of trigonometry by heart. This will help you gain speed and confidence in solving problems like these.
Solution:
Consider △ABC, where m∠B is 90°.
fig. 1
∴ From cotAcotAReplacing ∴ 15⋅cot A=8cot A=158−−−(1)fig. 1,=Opposite side to ∠AAdjacent side to ∠A=BCABthis in equation (1)BCAB=158−−−(2)[from figure]
From equation (2), we can say that AB=8x and BC=15x.
Wondering why we have taken "8x" and "15x" here ?
Check this video for understanding it.
Applying Pythagoras theorem on △ABC to find the value of AC, we get
AC2∴ AC2∴ AC2∴ AC=AB2+BC2=(8x)2+(15x)2=64x2+225x2=289x2=(17x)2=17x−−−(3)
Now,
sin Asin A=HypotenuseOpposite side to ∠A=ACBC=17x15x∴ sin A=1715
sec A=Adjacent side to ∠AHypotenuse=ABAC=8x17x∴ sec A=817
Without doing more calculation on paper, can you find the values of tan A, cos A and cosec A? Let us know your answers in comments below and also how you got the values without calculation.
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