Solving Trigonometry Equations and Problems with Examples and Tips

Evaluating $\prod_{{k = 1}}^{100} [1 + 2 \cos \frac{2 π \cdot 3^{k}}{3^{100} + 1}]$

Kendall Daniels 2022-04-03

Evaluating $lim_{x \to 0} \frac{\cos (a x) - \cos (b x)}{\sin^{2} (x)}$

aidinacol7 2022-04-03

Evaluating $lim_{x \to 0} \frac{1 - \cos x}{{(2 x)}^{2}}$
I have this question in my book and the answer amounts to $\frac{1}{4}$ . I don't see how, and I think it's an error. Can you confirm it is an error?
$lim_{x \to 0} \frac{1 - \cos x}{{(2 x)}^{2}}$
I assume it would need to be $\cos^{2} x$ instead.

alparcero97oy 2022-04-03

Evaluating $(\cot \frac{π}{18} - 3 \cot \frac{π}{6}) \cdot (\csc \frac{π}{9} + 2 \cot \frac{π}{9})$
Try:
$\cot \frac{π}{18} \csc \frac{π}{9} - 3 \sqrt{3} \csc \frac{π}{9} + 2 \cot \frac{π}{18} \cot \frac{π}{9} - 6 \sqrt{3} \cot \frac{π}{9}$

rhedynogh0rp 2022-04-03

Evaluate $\cos [(\frac{1}{2}) [\arcsin (- \frac{3}{5})]]$

Pizzadililehz 2022-04-03

Evaluate
$\sum_{n = 1}^{38} \sin (\frac{n^{8} π}{38})$

alparcero97oy 2022-04-03

Evaluate an integral of the form
$\int \cos (ω t) \ln \cos (ω t) d t$

Rolando Wade 2022-04-03

Equivalent of $\frac{\sin (x)}{x} = \sin c (x)$ for $\frac{\cos (x) - 1}{x}$

jisu61hbke 2022-04-03

Does the identity $\cos^{2} (x) + \sin^{2} (x) = 1$ hold in a unital Banach algebra where 1 is the unit?
Let's assume that we have an unital Banach algebra T and we define sine and cosine using the normal power series definition as for $R$ . Let $x \in T$ and let 1 be the unit of T. Does the Pythagorean trigonometric identity $\cos^{2} (x) + \sin^{2} (x) = 1$ still hold?

amantantawq5l 2022-04-03

Task is to find
$\prod_{k = 0}^{\infty} \cos (x \cdot 2^{- k})$

Polchinio3es 2022-04-03

Solving trigonometry equation
$3 \sin^{2} x - 3 \cos^{2} x + \cos x - 1 = 0$

Marzadri9lyy 2022-04-03

Solving the equation:
$3 \cos x - \sin 2 x = \sqrt{3} (\cos 2 x + \sin x)$

Petrolovujhm 2022-04-03

Solving $2 \sin (θ + 17) = \frac{\cos (θ + 8)}{\cos (θ + 17)}$

amonitas3zeb 2022-04-03

Solving $\sin (\frac{x}{x^{2} + 1}) + \sin (\frac{1}{x^{2} + x + 2}) = 0$
Here is my way:
First write the equation as
$\sin (\frac{x}{2 (x^{2} + 1)} + \frac{1}{2 (x^{2} + x + 2)}) \cos (\frac{x}{2 (x^{2} + 1)} - \frac{1}{2 (x^{2} + x + 2)}) = 0$
Then the real solution can be find by
$\frac{x}{2 (x^{2} + 1)} + \frac{1}{2 (x^{2} + x + 2)} = 0$
which gives x=-1.

Hanzikoval1pa 2022-04-03

Solving $\sqrt{2} = \frac{\cos (x)}{\cos (2 x)}$
for $0 \leq {x} \leq {2 π}$ ? I can't find any trigonometric identity to solve it.

Pasegeabe85xy 2022-04-03

Solving $\sin 3 x \cdot \cos 3 x = \sin 2 x$

smaakt4ucq 2022-04-03

Solving $\sin \frac{12}{x} = - 3 \cos 2 x$

Alexis Alexander 2022-04-03

Solving for x, $\sin^{10} x + \cos^{10} x = \frac{29}{16} \cos^{4} 2 x$
I had found the answer as $4 x = \frac{π}{2} + n π \Rightarrow x = \frac{π}{8} + \frac{n π}{4}$ where $n \in Z$ . However, I'm not sure whether or not it seems correct.

Jasmine Todd 2022-04-02

Find all solutions of the equation in the interval $[0, 2 π)$ . Express your answer in terms of k, where k is any integer.
$\tan 3 θ + 1 = \sec 3 θ$

Kendall Daniels 2022-04-02

Express as function of $z : \sin (a^{2} + b^{2}) + \cos (a^{2} + b^{2}) i$
Where z=a+bi
and
$f (a + b i) = \sin (a^{2} + b^{2}) + \cos (a^{2} + b^{2}) i$
How could I write this in terms of z?
f(z)=?

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