Question

5) Given TanA=7/24, Calculate the values of all trigonometric ratios and verify the following Pythagoras Identities.​

Answer 1

Answer:

Step-by-step explanation:

Let us draw a ∆ OMP in which ∠M = 90°.

Then sin θ = MP/OP = 8/17.

Let MP = 8k and OP = 17k, where k is positive.

By Pythagoras’ theorem, we get

OP2 = OM2 + MP2

⇒ OM2 = OP2 – MP2

⇒ OM2 = [(17k)2 – (8k)2]

⇒ OM2 = [289k2 – 64k2]

⇒ OM2 = 225k2

⇒ OM = √(225k2)

⇒ OM = 15k

Therefore, sin θ = MP/OP = 8k/17k = 8/17

cos θ = OM/OP = 15k/17k = 15/17

tan θ = Sin θ/Cos θ = (8/17 × 17/15) = 8/15

csc θ = 1/sin θ = 17/8

sec θ = 1/cos θ = 17/15 and

cot θ = 1/tan θ = 15/8.

Answer 2

Answer:

Tan A = 7/24 = opp / adj = BC / AB

Accg. to Pythagoras theorem

AC²= AB² + BC²

AC² = 24² + 7²

AC² = 576 + 49

AC² = 625

AC = √625

AC = 25 cm

Sin A = AB / AC

Sin A = 24/25

Cos A = 7/25

cosec A = 25/24

sec A = 25/7

Cot A = 24/7

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