Solving Trigonometry Equations and Problems with Examples and Tips

Prove formula for $\int \frac{d x}{(1 + x^{2})^{n}}$

dglennuo 2022-05-21

How is this trigonometric identify proven?
When researching answers to prove my identity
$\frac{\cos y}{1 - \sin y}$
I get to the point of
$\frac{1 + \sin y}{\cos y}$
Then it jumps straight to
$\sec y + \tan y$
How do you prove that identity?

ownerweneuf 2022-05-21

How can we bound $\frac{\sin (θ) \cos (θ)}{| \cos (θ) | + | \sin (θ) |}$

Jaycee Mathis 2022-05-21

Solving $\sin^{2} θ + \cos θ = 1$

shelohz0 2022-05-21

Show trigonometric identity $\frac{1 - \tan \frac{θ}{2}}{1 + \tan \frac{θ}{2}} = \sec θ - \tan θ$

Ashly Harrell 2022-05-20

the following formula can be found in the literature: $| \sin (z) |^{2} = \sin (x)^{2} + \sinh (y)^{2}$ , z=x+iy; $x, y \in R$ .
I am wondering if there is a similar formular in polar coordinates, i.e. $| \sin (r \cdot e^{i θ}) | = . . . ?$

Hayley Sanders 2022-05-20

Problem:
$\int_{0}^{τ} \sqrt{2} \cos^{4} (θ) + 3 \cos^{2} (θ) + 7 d θ$

Mauricio Hayden 2022-05-20

Show that
$f (x) = \sum_{k = - \infty}^{\infty} c_{k} e^{- i k x} = \frac{2 \sinh (π)}{π} \sum_{k = 1}^{\infty} \frac{(- 1)^{k - 1} k}{1 + k^{2}} \sin (k x)$
where $c_{k} = \frac{1}{4 π} \int_{- π}^{π} e^{i k x} (e^{x} - e^{- x}) d x$

Camille Flynn 2022-05-20

Derive the following identity:
$\tan (3 x) = \frac{3 \tan (x) - \tan^{3} (x)}{1 - 3 \tan^{2} (x)}$

Nylah Burnett 2022-05-20

Show that $\frac{1 + \sin A}{\cos A} + \frac{\cos B}{1 - \sin B} = \frac{2 \sin A - 2 \sin B}{\sin (A - B) + \cos A - \cos B}$

Nicholas Cruz 2022-05-20

Spotting substitution in $\int \frac{1}{(t + \cos α)^{2} + \sin^{2} α}$

Marianna Stone 2022-05-20

If $y = 9 \sec^{2} x + 16 \csc^{2} x$ ,find the minimum value of y , $y, \forall x \in R$

Denisse Valdez 2022-05-20

How to calculate $\sum_{k = 0}^{n} a^{k} \sin (k x)$ ?

Jazmine Bruce 2022-05-20

Which value is correct for $\sin^{- 1} (\frac{- \sqrt{3}}{2})$ , $\frac{4 π}{3}$ or $\frac{5 π}{3}$ ?
As far as I remember, both $\frac{4 π}{3}$ and $\frac{5 π}{3}$ are correct for the exact values of $\sin^{-} 1 (\frac{- \sqrt{3}}{2})$ . In symbolab and wolfram, they both showed $\frac{- π}{3}$ , which is equivalent to $\frac{5 π}{3}$ . But in other websites, it's $\frac{4 π}{3}$ . I really got confused. I remember my teacher in Precalculus, she said it's $\frac{4 π}{3}$ . I am now confused. Which is correct?

Anthony Kramer 2022-05-19

Let $a, b, c \in [0; \frac{π}{2}]$ such that
$\cos a = a; \sin \cos b = b; \cos \sin c = c .$
Put the numbers a,b,c in ascending order

osmane5e 2022-05-19

Why does $\sum_{n = 1}^{\infty} \frac{\cos \frac{1}{n}}{n}$ diverge but $\sum_{n = 1}^{\infty} \frac{\sin \frac{1}{n}}{n}$ converges?

realburitv4 2022-05-19

show that $\sin 15^{\circ} = \frac{\sqrt{3} - 1}{2 \sqrt{2}}$ using $\cos 2 A = 1 - 2 \sin^{2} A$ However I got $\sin 15^{\circ} = \sqrt{\frac{2 - \sqrt{3}}{4}}$ instead.

Brice Colon 2022-05-19

x , y & z are real number such that
$\frac{\sin x + \sin y + \sin z}{\sin (x + y + z)} = \frac{\cos x + \cos y + \cos z}{\cos (x + y + z)} = 2$
find the value
$\sum_{c y c} \sin x \sin y$

ownerweneuf 2022-05-19

Verify $\frac{\cot x - \tan x}{\cos x + \sin x} = \frac{\cos x - \sin x}{\sin x \cos x}$

tilfaen4a 2022-05-19

Deduce $\tan (π - x) = - \tan x$

The majority of Trigonometry Math problems are quite easy to solve when you have the list of answers that help you see the logic and reasoning. Looking at various examples will help you to see how certain questions are related to provided solutions.

Remember that Trigonometry requires patience and analysis. By following your analysis skills, you will help yourself find the answers. If something remains unclear, start with your exploration of examples again and go step-by-step.

Precalculus

Practice Exercises for Trigonometry