Maths / Introduction to Trigonometry / Trigonometric Ratios

QUESTION

Given  $\dpi{120} \fn_jvn \large cos\Theta =\frac {3}{5},$  calculate the values of the other five trigonometric ratios.

EXPLANATION
Explain TypeExplanation Content
Text

Recall that

$cos\Theta =\frac {base}{hypotenuse}$

So we draw a right triangle with right angle at C and with base BC = 3cm and hypotenuse AB = 5cm. To find AC, we use the Pythagorean theorem.

$AB^2=AC^2+BC^2$

$\Rightarrow$                                      $5^2=AC^2+3^2$

$\Rightarrow$                                     $AC^2=5^2-3^2=16$

$\Rightarrow$                                     $AC=4cm$

Now,                                  $sin\Theta =\frac {perpendicular}{hypotenuse}=\frac {AC}{AB}=\frac {4}{5}$

$tan\Theta =\frac {perpendicular}{base}=\frac {4}{3}$

$cot \Theta =\frac {1}{tan\Theta }=\frac {3}{4}$

$sec\Theta =\frac {1}{cos\Theta }=\frac {5}{3}$

and                                   $cosec\Theta =\frac {1}{sin\Theta }=\frac {5}{4}$

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