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Mathematics · Introduction to Trigonometry · NCERT Examples

Example 1

A complete, independently verified solution for NCERT Example 1.

Mathematics · Chapter 8 · NCERT Examples

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NCERT Example

Example 1

trigonometric ratios · Pythagoras theorem

Given tan A = 4/3, find the other trigonometric ratios of angle A.

Right triangle ABC, right-angled at B, with AB equal to 3k and BC equal to 4k.
Figure 8-8 from the supplied NCERT chapter.

Solution

Board-exam working:

tan⁡A=BCAB=43\tan A=\frac{BC}{AB}=\frac43

Let BC = 4k and AB = 3k.

AC=AB2+BC2=(3k)2+(4k)2=5kAC=\sqrt{AB^2+BC^2}=\sqrt{(3k)^2+(4k)^2}=5k
sin⁡A=BCAC=45\sin A=\frac{BC}{AC}=\frac45
cos⁡A=ABAC=35\cos A=\frac{AB}{AC}=\frac35
cot⁡A=34\cot A=\frac34
cosec⁡A=54\cosec A=\frac54
sec⁡A=53\sec A=\frac53

Final answer

sin⁡A=45, cos⁡A=35, cot⁡A=34, cosec⁡A=54, sec⁡A=53\sin A=\frac45,\ \cos A=\frac35,\ \cot A=\frac34,\ \cosec A=\frac54,\ \sec A=\frac53