Solving Trigonometry Equations and Problems with Examples and Tips

Evaluating: $\int \frac{1 + \sin (x)}{1 + \cos (x)} d x$

siliciooy0j 2022-04-02

Evaluating $\prod_{i = 1}^{60} \sin (3 i - 2) \sin (3 i - 1)$

Nathanael Hansen 2022-04-02

Evaluate: $lim_{x \to 0} \frac{\sin^{3} x - x^{3} s g n (1 - [\frac{x}{\sin^{- 1} x}])}{x \tan^{2} x \sin (π \cos x)}$
(Note that here sgn denotes the Signum function and [x] denotes the greatest integer less than or equal to x.)
The above simplifies to:
$lim_{x \to 0} \frac{\sin^{3} (x) - x^{3}}{x \tan^{2} (x) \sin (π (1 - \cos x))}$

fsrlaihq55 2022-04-02

Evaluate the indefinite integral
$\int \frac{\csc^{2} x - 2005}{\cos^{2005} x} d x$

siliciooy0j 2022-04-02

Evaluate $\int \frac{1}{x^{2} + 9} d x$

monkeyman130yb 2022-04-02

Evaluate $\int_{C} \frac{\cos (z)}{z^{2} + 1} d z$ where the contour C is the circle of radius 5 centred at 0.

Coradossi7xod 2022-04-02

The following function models the length L of each day (in minutes) in Manila, t days after the spring equinox, which is March 22.
$L (t) = 52 \sin (\frac{2 π t}{365}) + 728$
What is the first time after March 22 that the day length hits 700 minutes?

Marzadri9lyy 2022-04-02

The equality I'm trying to prove looks like that:
${\tan 40}^{\circ} + \sqrt{3} = 4 {\sin 40}^{\circ}$

Lesnaoq73 2022-04-02

Testing with my calculator in degree mode, I have found the following to be true:
$\tan (90 - \frac{1}{10^{n}}) \approx \frac{180}{π} \times 10^{n}, n \in N$

Asher Olsen 2022-04-02

Suppose the minimum value of $\cos^{2} θ (θ_{1} - θ_{2}) + \cos^{2} (θ_{2} - θ_{3}) + \cos^{2} (θ_{3} - θ_{1})$ is $\frac{3}{4}$

ab0utfallingm1z2 2022-04-02

Sum of real solutions on equation
$\sqrt{\sin^{2} x + \frac{1}{2}} + \sqrt{\cos^{2} x + \frac{1}{2}} = 2$ in interval $[0, 2 π]$ is ?

acidizihvzs 2022-04-02

solving $y^{″} + y = \sec (x)$

Hanzikoval1pa 2022-04-02

Solving $2 \cos 2 x - 4 \sin x \cos x = \sqrt{6}$

ideklaraz7xz 2022-04-02

Solving $2 \sin^{2} x + 6 \sin^{2} \frac{12}{x} = 3$
Find the angles between $0^{\circ} and 360^{\circ}$ which satisfy the equation above.
So, I found the answers by inputting all the possible special angles; $60^{\circ} and 120^{\circ}$ worked.
Are there any other ways to find the answers, and are there more than the two answers that I found?

justbethlflql 2022-04-02

Solving $\sin (3 x + 28^{\circ}) = \cos (2 x - 13^{\circ})$
Solution:
3x+28+2x-13=90
x=15
3x+28-2x+13=90
x=49
But the value
x=87
also satisfies the equation. I do not know how it comes.

Rex Maxwell 2022-04-02

Solving $\cos x + \cos 2 x - \cos 3 x = 1$ with the substitution $z = \cos x + i \sin x$

Aryan Salinas 2022-04-02

Solving for k in $\cos \frac{π}{k} - \cos \frac{2 π}{k} = P$

annlanw09y 2022-04-02

Prove that $\frac{1 + \sin θ + i \cos θ}{1 + \sin θ - i \cos θ} = \sin θ + i \cos θ$

Lorelei Stanton 2022-04-02

Prove that
$\sin^{2} α + 4 \sin^{4} \frac{α}{2} = 4 \sin^{2} \frac{α}{2}$

ropowiec2gkc 2022-04-02

Prove that
$1 + m \cos 2 θ + (\begin{matrix} m \\ 2 \end{matrix}) \cos 4 θ + \dots + (\begin{matrix} m \\ r \end{matrix}) \cos 2 r θ + \dots + \cos 2 m θ = 2^{n} \cos^{m} θ \cos m θ$

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