Recent questions and answers in Trigonometry & Complex Numbers

Evaluate : $\large\frac{10+2i}{(3+i)(3-i)}\qquad (i=\sqrt{-1})$

answered Jan 11, 2020 by priyanka.clay6

1 answer

If $i=\sqrt{-1}$, what is the value of $i^{24}+i^{32}$

answered Jan 8, 2020 by priyanka.clay6

1 answer

If $\sin \theta - \cos \theta = \frac{1}{2},$ then the value of $\large\frac{1}{\sin \theta + \cos \theta} = $

answered Jan 8, 2020 by priyanka.clay6

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The length of the shadow of a $60$ feet tall building is $60\sqrt{3}$. What can be the angle of elevation of the Sun ?

answered Jan 6, 2020 by priyanka.clay6

1 answer

If $i=\sqrt{-1},$ then what is the value of $(i)^{729}$

answered Jan 3, 2020 by priyanka.clay6

1 answer

If $\sin^2 \theta+ \cos^2 \theta = 1$, then what is $\sec \theta$ in terms of $\sin \theta$ ?

answered Jan 1, 2020 by priyanka.clay6

1 answer

Solve: $\tan \bigg(\large\frac{5 \pi}{3}\bigg)$ equals

answered Dec 30, 2019 by priyanka.clay6

1 answer

If $i=\sqrt{-1},$ then find the value of $(i^{89}+i^{72})^3$

answered Dec 22, 2019 by priyanka.clay6

1 answer

ABC is a right angled triangle, right angled at $C$. If $CB= 3\;cm$ and the length are $3cm,\;4 cm\;$ and $5\;cm$, which trigonometric ratio of $\angle A$ is greatest ?

answered Dec 22, 2019 by priyanka.clay6

1 answer

If $i=\sqrt{-1}$, then evaluate $(3i+9)(2i-8)$

answered Dec 19, 2019 by priyanka.clay6

1 answer

In a right triangle, one angle measures $x^{\circ}$ where $\sin x = \large\frac{4}{5},$ what is the $\cos (90^{\circ}-x).$ ?

answered Dec 18, 2019 by priyanka.clay6

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If $7 \sin^2 \theta + 3 \cos^2 \theta = 4,$ then $\tan \theta=$

answered Dec 18, 2019 by priyanka.clay6

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Jare's house is in front of a $20\;m$ high tower. It cents a shadow on the ground, which is $20\sqrt{3}\;m$ long. What can be the sum altitude ?

answered Dec 16, 2019 by priyanka.clay6

1 answer

If $\cos \theta =\frac{a}{b}$, then $\mathrm{cosec }\; \theta=$

answered Dec 16, 2019 by priyanka.clay6

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If $i=\sqrt{-1}$, then what can be the value of $(i^{32})^{64}$

answered Dec 13, 2019 by priyanka.clay6

1 answer

Whenever $\cos \theta =0$ and $0 \leq \theta \leq \pi$, the value of $\sin \theta = $

answered Dec 13, 2019 by priyanka.clay6

1 answer

Find the value of $(6-2i)(3-5i)$

answered Dec 12, 2019 by priyanka.clay6

1 answer

What is $i^{128}$?

answered Dec 11, 2019 by priyanka.clay6

1 answer

If $i=\sqrt{-1} $ then $(i^2+i)(i^4-i^2)=$

answered Dec 6, 2019 by priyanka.clay6

1 answer

A kite is flying at a height 30 m from the ground. The length of the string from the kite to the ground is 60 m. Assuming that there is no slack in the string, find the angle of elevation of the kite at the ground.

answered Dec 6, 2019 by priyanka.clay6

1 answer

If $i=\sqrt{-1}$, then evaluate $(7-3i)(7+3i)$

answered Dec 3, 2019 by priyanka.clay6

1 answer

$\begin{align}\large\frac{(i^3)^{729}}{(i^4)^{64}} = \end{align}$

answered Dec 2, 2019 by priyanka.clay6

1 answer

If $f(y)=\tan y+ \cot y$, then the value of $f(\large\frac{\pi}{4})$ is

answered Dec 1, 2019 by priyanka.clay6

1 answer

Which of the following expressions is equivalent to $(6+5i)^3$

answered Nov 28, 2019 by priyanka.clay6

1 answer

If $(2+4i)(5-ki)=50$, then the value of $k$ is

answered Nov 26, 2019 by priyanka.clay6

1 answer

In trapezium $ABCD$, if $AB = 9\; cm, DC = 6\; cm$ and $BD = 12\; cm$, then $BO$ is equal to

answered Nov 26, 2019 by priyanka.clay6

1 answer

If $\begin{align}\frac{\sin \theta + \cos \theta}{\sin \theta - \cos \theta} = \frac{\sqrt{3}+1}{\sqrt{3}-1} \end{align}$, then the acute angle $\theta$ is

answered Nov 25, 2019 by priyanka.clay6

1 answer

In the figure given $\tan a = x$. What is the value of $\cos b$ ?

answered Nov 18, 2019 by priyanka.clay6

1 answer

If $i=\sqrt{-1}$, what is the value of $(i+3)(i-\frac{1}{2})?$

answered Nov 18, 2019 by priyanka.clay6

1 answer

$(i^{100})^{25} = $

answered Nov 18, 2019 by priyanka.clay6

1 answer

Elina wanted to build a ramp for her elderly cat, polly walk up to her bed. She needs the ramp to make an angle of $30^\circ$ with the bedroom floor. How long must the ramp be to reach the top of her bed that is exactly three feet above the ground ?

answered Nov 17, 2019 by priyanka.clay6

1 answer

For $i = \sqrt{-1}\;$, Evaluate $\frac{7+3i}{7-3i}$

answered Nov 4, 2019 by priyanka.clay6

1 answer

$\cot (-300)=$

answered May 28, 2019 by meena.clay6

1 answer

If $0 < x< \large\frac{\pi}{2}$ and $\large\frac{\cos x}{1-\sin^2x} = \frac{5}{2}$, what is the value of $\cos x$?

answered May 28, 2019 by meena.clay6

1 answer

Find the value of $cosec \bigg(\large\frac{2\pi}{3}\bigg)$

answered May 28, 2019 by meena.clay6

1 answer

If $i=\sqrt{-1}$ then what is the value of $(i)^{128}$

answered May 23, 2019 by meena.clay6

1 answer

$\Delta XYZ$ is a right angled triangle , right angled at Y as shown in figure . What is the value of the difference of $\sin 60^{\circ}$ and $\cos 30^{\circ}$ if the ratio of the sides are $1: \sqrt 3:2$

answered May 8, 2019 by meena.clay6

1 answer

Solve: $\large\frac{(2+3i)(2-3i)}{1-i}=$

answered May 7, 2019 by meena.clay6

1 answer

Given below is a triangle one of the acute angles is $60^{\circ}$. The base of the triangle is given as 15 cm. What is its height ?

answered Apr 29, 2019 by meena.clay6

1 answer

In the figure below, the circle with centre $o$ has $OA = 4$ and $BC =2$, What is the value of $x$? <br><br>

answered Apr 28, 2019 by priyanka.clay6

1 answer

What is the length of each side of a square, if its diagonal is 15 ?

answered Apr 25, 2019 by priyanka.clay6

1 answer

In the XY plane above , O is the center of the circle. The measure of $\angle AOX$ is

answered Apr 12, 2019 by meena.clay6

1 answer

Value for $((i^4)^8)^{10}$ is

answered Apr 7, 2019 by priyanka.clay6

1 answer

If a complex number coincides with its conjugate then the number must lie on

answered Apr 5, 2019 by priyanka.clay6

1 answer

The value for $\frac{1-i}{1+i} $ is

answered Apr 4, 2019 by priyanka.clay6

1 answer

If $i =\sqrt{-1}$, what can be the value of $\dfrac{(3+i)(2-i)}{3-i } $ is

answered Apr 2, 2019 by priyanka.clay6

1 answer

If the complex number $A$ satisfies the equation $A(3-i) = 2 + i$, where $i = \sqrt{-1}$, what is the value of $A$.

answered Apr 1, 2019 by priyanka.clay6

1 answer

If $\cos x = a$ where $\frac{\pi}{2} < x < \pi$, and $\cos y = -a$, then which of the following could be the value of $y$ ?

answered Apr 1, 2019 by priyanka.clay6

1 answer

If $( \cos x) (\sin x) = 0.5$, what is the value of $(\cos x + \sin x)^2 $

answered Apr 1, 2019 by priyanka.clay6

1 answer

Convert $210^{\circ}$ to radian

answered Apr 1, 2019 by meena.clay6

1 answer

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