Question
If $\tan = 0.75,$ find the other trigonometric ratios for $A.$
✓
Answer
$\tan A =0.75=\frac{75}{100}=\frac{3}{4}=\frac{\text { Perpendicular }}{\text { Base }} $
Hypotenuse
$=\sqrt{(\text { Perpendicular })^2+(\text { Base })^2} $
$=\sqrt{3^2+4^2} $
$=\sqrt{9+16} $
$=\sqrt{25} $
$=5 $
$\sin A =\frac{\text { Perpendicular }}{\text { Hypotenuse }}=\frac{3}{5}=0.6 $
$\cos A =\frac{\text { Base }}{\text { Hypotenuse }}=\frac{4}{5}=0.8 $
$\operatorname{cosec} A =\frac{1}{\sin A }=\frac{5}{3}=1.66 $
$\sec A =\frac{1}{\cos A }=\frac{5}{4}=1.25 $
$\operatorname{cost} A =\frac{1}{\tan A }=\frac{4}{3}=1.33 .$
Hypotenuse
$=\sqrt{(\text { Perpendicular })^2+(\text { Base })^2} $
$=\sqrt{3^2+4^2} $
$=\sqrt{9+16} $
$=\sqrt{25} $
$=5 $
$\sin A =\frac{\text { Perpendicular }}{\text { Hypotenuse }}=\frac{3}{5}=0.6 $
$\cos A =\frac{\text { Base }}{\text { Hypotenuse }}=\frac{4}{5}=0.8 $
$\operatorname{cosec} A =\frac{1}{\sin A }=\frac{5}{3}=1.66 $
$\sec A =\frac{1}{\cos A }=\frac{5}{4}=1.25 $
$\operatorname{cost} A =\frac{1}{\tan A }=\frac{4}{3}=1.33 .$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
In the following figures, find the remaining angles of the parallelogram
During every financial year, the value of a machine depreciates by $12\%.$ Find the original cost of a machine which depreciates by $Rs. 2,640$ during the second financial year of its purchase.
→Explain the meaning of the following terms: True Class Limits
Find the value of $k$ in each of the following:$(\sqrt{9})^{-7} \times(\sqrt{3})^{-5}=3^k$
→Solve the following:$\log (x + 1) + \log (x - 1) = \log 48$
→Factorise :$a^6- 7a^3- 8$
→→
Prove that : $\left(\frac{x^a}{x^b}\right)^{(a+b)} \cdot\left(\frac{x^b}{x^c}\right)^{(b+c)} \cdot\left(\frac{x^c}{x^a}\right)^{(c+a)}=1$.
→If $x+2 y+3 z=0$ and $x^3+4 y^3+9 z^3=18 x y z;$ evaluate $:\frac{(x+2 y)^2}{x y}+\frac{(2 y+3 z)^2}{y z}+\frac{(3 z+x)^2}{z x}$
→In the given figure, $D , E , F$ are the mid-points of the sides $B C, C A$ and $A B$ respectively.
(i) If $AB =6.2 cm$, find DE .
(ii) If $DF =3.8 cm$, find AC .
(iii) If perimeter of $\triangle A B C$ is 21 cm , find FE .
→(i) If $AB =6.2 cm$, find DE .
(ii) If $DF =3.8 cm$, find AC .
(iii) If perimeter of $\triangle A B C$ is 21 cm , find FE .