Practice Trigonometric Functions Problems

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Trigonometry
Trigonometric Functions

Recent questions in Trigonometric Functions

Rosemary Chase 2022-11-07

$\sin (A) + \cos (A) = 1 / 4$ . Find $\sin (A) \cos (A)$ without a calculator. I think it is about double angles formula $\sin (2 A) = 2 \sin A \cos A$ but I still didn't know how to solve it.

Demarion Ortega 2022-11-07

How do you solve $\cos (3 x) = \cos (x)$ ?
I have tried to rewrite it to 4cos3(x)−3cos(x)=cos(x) and then solve it. Add 3cos(x) to both sides and then divide by 4. And then I have this: cos3(x)=cos(x) . I don’t know what so do now or even if on the right track.

Owen Mathis 2022-11-07

Solving $\sqrt{\frac{11 \cdot \sin (x)^{2} - 2}{\sin (x)^{2}} + 5 \cdot \cot (x)} = 3 - \cot (x)$

Clara Dennis 2022-11-06

How to solve $s i n (x) = n$ for all $n \in R$ ?
I was wondering how one would solve the equation $s i n (x) = n$ for all real n. You could of course use the Taylor series of $s i n^{- 1} (x)$ but that wouldn't give an exact result.
So I thought maybe you can use Euler's formula for $s i n (x)$ ( $s i n (x) = \frac{e^{i x} - e^{- i x}}{2 i}$ ) to get an exact result?

undergoe8m 2022-11-06

If $\tan θ + \sin θ = m$ and $m^{2} - n^{2} = 4 \sqrt{m n}$ so prove that $\tan θ - \sin θ = n$
we have to take $4 \sqrt{m (\tan θ - \sin θ)} = 4 \sqrt{m n}$ to satisfy $\tan θ - \sin θ = n$ but I don't like it, I just want direct derivation.

Ty Moore 2022-11-06

Compute the indefinite integral
$\int \sqrt{\frac{e^{n x}}{e^{n x} + 1}} d x : n \in Z^{*}$

Messiah Sutton 2022-11-06

How do i prove this $\frac{\sin^{2} (20)}{\sin (140) \sin (80)} = \frac{\cos (80)}{\cos (20)}$

perlejatyh8 2022-11-05

Find the number of solutions to the equation $\sin (\frac{π \sqrt{x}}{4}) + \cos (\frac{π \sqrt{2 - x}}{4}) = \sqrt{2}$

MMDCCC50m 2022-11-05

How to do the following trigonometric simplification: $\frac{1 - \cos (3 α)}{1 - \cos (α)} = (1 + 2 \cos (α)^{2})$

trumansoftjf0 2022-11-05

Is it hard to tackle the integral $\int_{0}^{\infty} \frac{x^{2}}{{(1 + x^{4})}^{2}} d x ?$

Elliana Molina 2022-11-05

Calculate:
$\frac{d}{d x} \sin^{2} x \cos^{3} x$

Karley Castillo 2022-11-05

Solve $\sin (z) = \frac{3 + i}{4}$
What i did so far was this:
$\sin (z) = \frac{3 + i}{4} \Rightarrow \frac{e^{i z} - e^{- i z}}{2 i} = \frac{3 + i}{4} \Rightarrow e^{2 i z} - 1 = (\frac{- 1 + 3 i}{2}) e^{i z}$
setting $u = e^{i z}$ we'll have
$u^{2} + (\frac{1 - 3 i}{2}) u - 1 = 0$
completing squares
${(u + \frac{1 - 3 i}{4})}^{2} = \frac{3}{8} (1 + i)$
seting $w = u + \frac{1 - 3 i}{4}$
$w^{2} = \frac{3}{8} (1 + i)$
solving
$w = \pm 2^{\frac{- 5}{4}} \sqrt{3} (\cos (\frac{\sqrt{2}}{4}) + i \sin (\frac{\sqrt{2}}{4}))$
now i just have to substitute this in $w = u + \frac{1 - 3 i}{4}$ and then in $u = e^{i z}$ , but the solution looks really big . So what did i do wrong?

spasiocuo43 2022-11-04

Prove that $\cot 99^{\circ} = 3 \cot 36^{\circ} - \sec 18^{\circ} - \csc 18^{\circ}$

inurbandojoa 2022-11-04

Solve trigonometric inequality $2 \cos^{2} x + \cos (2 x) \geq 1$
My attempt:
$2 \cos^{2} x + \cos^{2} x - \sin^{2} x \geq \sin^{2} x + \cos^{2} x$
$2 \cos^{2} x - 2 \sin^{2} x \geq 0$
$2 (\cos^{2} x - \sin^{2} x) \geq 0$
$2 \cos (2 x) \geq 0$
$\cos (2 x) \geq 0$
What`s next?

Nicholas Hunter 2022-11-04

Determine the value of the expression $\frac{5}{\sin^{2} A} + \frac{7}{\cos^{2} B}$ if $\cos A = \frac{- 2}{3}$ and $\sin B = \frac{3}{4}$

Frankie Burnett 2022-11-04

Evaluating $\int \frac{\sec^{2} (x)}{(4 + \tan^{2} (x))^{2}} d x$

Jonas Huff 2022-11-04

Is there any formula for $\arctan (a + b)$

Ayanna Goodman 2022-11-04

Calculate the value of
$\frac{\sin (56 π)}{\sin (14 π)}$
What is my mistake in the following calculations?

Brenda Jordan 2022-11-04

Showing that $\arctan (\cos (α) * \tan (x)) = \arccos (\frac{\cos (x)}{\cos (\arcsin (\sin (α) * \sin (x)))})$

Siemensueqw 2022-11-03

Evaluate $\int_{0}^{π} \log (5 - 4 \cos x) d x$

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