Maths / Introduction to Trigonometry / Trigonometric Ratios

QUESTION
 

Given  large cosTheta =frac {3}{5},  calculate the values of the other five trigonometric ratios.

EXPLANATION
Explain TypeExplanation Content
Text

Recall that

            cosTheta =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,                                  sinTheta =frac {perpendicular}{hypotenuse}=frac {AC}{AB}=frac {4}{5}

                                            tanTheta =frac {perpendicular}{base}=frac {4}{3}

                                            cot Theta =frac {1}{tanTheta }=frac {3}{4}

                                           secTheta =frac {1}{cosTheta }=frac {5}{3}

and                                   cosecTheta =frac {1}{sinTheta }=frac {5}{4}

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