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In the Following, One of the Six Trigonometric Ratios is Given. Find the Values of the Other Trigonometric Ratios. `Tan Theta = 8/15` - Mathematics

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Question

In the following, one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios.

`tan theta = 8/15`

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Solution

We know that `tan theta = "๐‘œ๐‘๐‘๐‘œ๐‘ ๐‘–๐‘ก๐‘’ ๐‘ ๐‘–๐‘‘๐‘’"/"๐‘Ž๐‘‘๐‘—๐‘Ž๐‘๐‘’๐‘›๐‘ก ๐‘ ๐‘–๐‘‘๐‘’" = 8/15`

Now consider a right-angled Δle ABC.

By applying Pythagoras theorem

๐ด๐ถ2 = ๐ด๐ต2 + ๐ต๐ถ2

๐‘ฅ2 = 82 + 152

๐‘ฅ2 = 225 + 64 = 289

`x  = sqrt289 = 17`

`sin theta = "๐‘œ๐‘๐‘๐‘œ๐‘ ๐‘–๐‘ก๐‘’ ๐‘ ๐‘–๐‘‘๐‘’"/"โ„Ž๐‘ฆ๐‘๐‘œ๐‘ก๐‘’๐‘›๐‘ข๐‘ ๐‘’" = 8/17`

`cos theta = "๐‘Ž๐‘‘๐‘—๐‘Ž๐‘๐‘’๐‘›๐‘ก ๐‘ ๐‘–๐‘‘๐‘’"/"โ„Ž๐‘ฆ๐‘๐‘œ๐‘ก๐‘’๐‘›๐‘ข๐‘ ๐‘’" = 15/17`

`tan theta = "๐‘œ๐‘๐‘๐‘œ๐‘ ๐‘–๐‘ก๐‘’ ๐‘ ๐‘–๐‘‘๐‘’"/"๐‘Ž๐‘‘๐‘—๐‘Ž๐‘๐‘’๐‘›๐‘ก ๐‘ ๐‘–๐‘‘๐‘’" = 8/15`

`cot theta = 1/tan theta = 1/(8/15) = 15/8`

`cosec theta = 1/sin theta = (1/8)/17 = 17/8`

`sec theta = 1/cos theta= (1/15)/17 = 17/15`

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Chapter 10: Trigonometric Ratios - Exercise 10.1 [Page 23]

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RD Sharma Mathematics [English] Class 10
Chapter 10 Trigonometric Ratios
Exercise 10.1 | Q 1.08 | Page 23

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