Maths / Introduction to Trigonometry / Reciprocal Trigonometric Ratios

QUESTION
 

If  cosTheta =frac {p}{q}, find the value of cosecTheta .

OPTIONS
A. 

large frac {q}{sqrt {q^2-p^2}}

B. 

large frac {sqrt {q^2-p^2}}{p}

C. 

Both a and b

D. 

None of these

Right Option : A

EXPLANATION
Explain TypeExplanation Content
Text

We know  cosTheta =frac {base}{hypotenuse}

We draw a right triangle, with right angle at C and having base BC = p and hypotenuse BA = q.

By the pythagorean theorem

                                                 AB^2=BC^2+AC^2

Rightarrow                                           q^2=p^2+AC^2

Rightarrow                                           AC^2=q^2+AC^2

Rightarrow                                          AC= sqrt {q^2-p^2}: : : : : : [therefore AC>0]

Thus,                           cosecTheta =frac {hypotenuse}{perpendicular }=frac {q}{sqrt {q^2-p^2}}

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