Question

State whether the following are true or false. Justify your answer.
(i) The value of $\tan A$ is always less than $1$.
(ii) $\sec A=\frac{12}{5}$ for some value of angle $A$.
(iii) $\cos A$ is the abbreviation used for the cosecant of angle $A$.
(iv) $\cot A$ is the product of $\cot$ and $A$.
(v) $\sin \theta =\frac{4}{3}$ for some angle $\theta$.

Answer 1

(i) False

$\angle B={90}^o$, $AB=3,BC=4,AC=5$

$\tan A=\frac{4}{3}>d$. ...$(A{C}^2=A{B}^2+B{C}^2)$

(ii) True

$A{C}^2=A{B}^2+B{C}^2$

$(12x{)}^2=(5x{)}^2+B{C}^2$,

$BC=\sqrt{119x}$

(it is possible) Pythagoras theorem

(iii) False

$\cos A$ is cosine $A$, $\csc A$ is cosecant

(iv) False

$\cot A$ = cotangent of $\angle A$ not product of $\cot$ and $A$.

(v) False

$\sin \theta =\frac{\text{perpendicular}}{\text{hypotenuse}}$

$\sin \theta >1$; $\frac{4}{3}>1$ [$\because$ hypotenuse > base > perpendicular]

$\sin \theta$ will always less than $1$.