Question

if tan theta =12/5 find all trigonometric ratios​

Answer 1

EXPLANATION.

Tan ø = 12/5 = p/b = perpendicular/Base.

By using the Pythagorean theorem we get,

→ H² = P² + B².

→ H² = (12)² + (5)².

→ H² = 144 + 25.

→ H² = 169.

→ H = √169.

→ H = 13.

→ Sin ø = p/h = 12/13.

→ Cos ø = b/h = 5/13.

→ Tan ø = p/b = 12/5.

→ Csc ø = h/p = 13/12.

→ Sec ø = h/b = 13/5.

→ Cot ø = b/p = 5/12.

More information.

→ Sin²A + Cos²A = 1.

→ Tan²A + 1 = Sec²A.

→ 1 + Cot²A = Csc²A.

Answer 2

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tan θ = O/A( Opposite/ Hypotenuse )

By Using Pythagoras Theorem,

--》H² = O² + A²

--》H² = 12² + 5²

--》H² = 144 + 25

--》H² = 169

--》H = √169

--》H = 13

--》Sin θ = O/H = 12/13 --》 (1)

--》Tan θ = O/A = 12/5 --》(2)

--》Cos θ = A/H = 5/13 --》(3)

--》Cot θ = A/O = 5/12 --》(4)

--》Sec θ = H/A = 13/5 --》(5)

--》Cosec θ = H/O = 13/12 --》(6)

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$\boxed{\begin{minipage}{6cm} Important Trigonometric identities :- \\ \\ \: \: 1)\:\sin^2\theta+\cos^2\theta=1 \\ \\ 2)\:\sin^2\theta= 1-\cos^2\theta \\ \\ 3)\:\cos^2\theta=1-\sin^2\theta \\ \\ 4)\:1+\cot^2\theta=\text{cosec}^2 \, \theta \\ \\5)\: \text{cosec}^2 \, \theta-\cot^2\theta =1 \\ \\ 6)\:\text{cosec}^2 \, \theta= 1+\cot^2\theta \\\ \\ 7)\:\sec^2\theta=1+\tan^2\theta \\ \\ 8)\:\sec^2\theta-\tan^2\theta=1 \\ \\ 9)\:\tan^2\theta=\sec^2\theta-1 \end{minipage}}$

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