Solving Trigonometry Equations and Problems with Examples and Tips

How to proof
$\arcsin (\sqrt{2 \cdot b \cdot (\sqrt{1 + b^{2}} - b)}) = \arccos (\sqrt{1 + b^{2}} - b)$

Mary Bates 2022-04-06

How to graph $f (x) = \frac{1 - \cos (2 x - 2)}{{(x - 1)}^{2}}$ analytically?
I only have an issue when it comes to determining the hole at $x = 1$ analytically. Graphing the function on a graphing utility reveals a hole at $x = 1$ rather than a vertical asymptote. I know that by simply plugging in the value $1$ for $x$ , one will see that both the numerator and denominator equate to zero. This shows that there is at least one factor of $(x - 1)$ that can be extracted from the numerator.
I would like to know how to simplify this function analytically in such a way that two factors of $(x - 1)$ can be obtained from the numerator. I believe one must make use of an inverse function down the line in order to extract the obvious $(x - 1)$ hiding in the $\cos (2 x - 2) = \cos (2 (x - 1))$ term. That is as far as I got in the problem.

Brielle James 2022-04-06

How to get $\frac{2}{t^{2} + 1}$ as the derivative for $\sin (θ)$ when $\tan (\frac{θ}{2}) = t$

Brooks Barker 2022-04-05

For n real numbers $x_{1}, x_{2}, \dots, x_{n}$ , consider
$a = \sin (x_{1}) \cos (x_{2}) + \sin (x_{2}) \cos (x_{3}) + \dots + \sin (x_{n}) \cos (x_{1})$
How do we find maximum value of a?
For what values of $x_{1}, x_{2} \dots ., x_{n}$ is the maximum achieved?
I want to get help from you If that's possible.

Hallie Watts 2022-04-05

Finding $\cos (\frac{π}{8})$ with half angle identities.

Yaritza Estrada 2022-04-05

Finding all values of $\sin (x - 50^{\circ}) = - 0.682$ between $0^{\circ}$ and $360^{\circ}$

ds522stlk 2022-04-05

Find value of $\tan 1 \times \tan 2 \times \dots \times \tan 89$ . Please don't answer, but please help me to figure this out this as I am not aware of any method to calculate this. I tried it by finding value of $\tan (90^{\circ})$ , but it didn't work as $\tan (90^{\circ})$ is not-defined.

Malachi Mullins 2022-04-05

Find value of $\tan (\frac{π}{25}) \cdot \tan (\frac{2 π}{25}) \dots \tan (\frac{12 π}{25})$
The solution I tried:
Assume
$P = \tan (\frac{π}{25}) \cdot \tan (\frac{2 π}{25}) \cdot \tan (\frac{3 π}{25}) \dots \dots \tan (\frac{12 π}{25})$ ,
with the help of $\tan (π - θ) = - \tan θ$ , then
$P = \tan (\frac{13 π}{25}) \cdot \tan (\frac{14 π}{25}) \cdot \tan (\frac{15 π}{25}) \dots \dots \tan (\frac{24 π}{25})$
which gives
$P^{2} = \prod_{{r = 1}}^{24} \tan (\frac{r π}{25})$

Ashleigh Mitchell 2022-04-05

Find the value(s) of $θ$ such that: $\sin (θ + 30^{\circ}) = {\cos 50}^{\circ}$

Joaquin Salas 2022-04-05

Find the value of $\sin (\frac{1}{4} \arcsin \frac{\sqrt{63}}{8})$

Haylee Bowen 2022-04-05

Find the value of F
${(\frac{1.5}{F})}^{2} + \cos^{2} (75) + {(\frac{1.25}{F})}^{2} = 1$

Miguel Hanson 2022-04-05

Find the value of
$({\cos 52}^{\circ} + {\cos 68}^{\circ} + {\cos 172}^{\circ})$

Quinn Moses 2022-04-05

Find the solutions of
$\sin z = 3$

poznateqojh 2022-04-05

Find the range of $f (x) = 11 \cos^{2} x + 3 \sin^{2} x + 6 \sin x \cos x + 5$
I have simplified this problem to
$f (x) = 8 \cos^{2} x + 6 \sin x \cos x + 8$
and tried working with $g (x) = 8 \cos^{2} x + 6 \sin x \cos x$

Rosa Townsend 2022-04-05

Find the $θ$ of $\frac{a}{\cos θ} + \frac{b}{\sin θ} = c$

Bryant Jacobs 2022-04-05

Find the product $\sec x \cdot \csc x$
To be $\frac{π}{2} < x < π$ . If
$\tan^{2} x + \cot^{2} x + 4 \tan x + 4 \cot x - 10 = 0$
find the product $\sec x \cdot \csc x$

jisu61hbke 2022-04-05

Find all solutions of the equation in the interval $[0, 2 π)$ (express your answer in terms of k, where k is any integer).
$\cos 2 θ + 7 \cos θ = 8$

Jaylin Clements 2022-04-05

Find a formula for $\sin (5 x)$ in terms of $\sin (x)$ and $\cos (X)$ .

nomadzkia0re 2022-04-05

Exact value $\sin (160^{\circ}) \sin (140^{\circ}) \sin (110^{\circ})$

Harold Hoover 2022-04-05

Evaluating $lim_{x \to 0} \frac{x}{\sin (\frac{1}{x^{2}})}$

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