Solving Trigonometry Equations and Problems with Examples and Tips

Can you help me solve this without using de l'Hôpital's rule (just using Standard rules):
$lim_{x \to 0} \frac{\sin x - x \cos x}{x^{3}}$

Beverley Rahman 2022-02-26

What is the number of real roots of the equation
$2 \cos (\frac{x^{2} + x}{6}) = 2^{x} + 2^{- x}$

trasbocohf1 2022-02-26

How would I prove the following double angle identity?
$\frac{\sin 2 A - \sin A}{\cos 2 A + \sin A} = \tan \frac{3 A}{2} \cdot \cot \frac{A}{2}$

SnuluddidaPalbx4 2022-02-26

Solve the following limit:
$lim_{x \to \frac{π}{6}} \frac{2 \sin (x) - 1}{\sqrt{3} \tan (x) - 1}$

Reginald Owens 2022-02-26

How do you determine the local extrema points for $y = \sqrt{3} \cos (3 x) + \sin (3 x)$ ?

Cobie Sadler 2022-02-26

I was asked to find the minimum and maximum values of the functions:
$1 . y = \frac{\sin^{2} x}{1 + \cos^{2} x}$
$2 . y = \sin^{2} x - \cos^{4} x$

Lubna Boyce 2022-02-26

In the equation:
$(a - b) \cot θ) \cos^{2} θ = - \frac{b}{2} \cot θ$

embeucadaoo8 2022-02-26

Show that
$\frac{\sin x}{\cos 3 x} = \frac{1}{2} (\tan 3 x - \tan x)$

Alexandria Dodd 2022-02-26

How do I prove the identity:
$\tan (\frac{π}{4} - x) = \frac{1 - \sin 2 x}{\cos 2 x}$

Gary Johnson 2022-02-26

Solve the equation:
$\sin^{2000} x + \cos^{2000} x = 1$

Umaiza Hutton 2022-02-26

The question is find the general solution of this equation:
$\sin (7 ϕ) + \cos (3 ϕ) = 0$

Richie Patterson 2022-02-26

Prove that
$\cos 2 θ - \sqrt{3} \sin 2 θ \equiv 2 \cos (2 θ + \frac{π}{3}) \equiv - 2 \sin (2 θ - \frac{π}{6})$

Brooklyn1wp 2022-02-26

Find the solution:
$\frac{1 + \tan (x) + \tan^{2} (x) + \dots + \tan^{n} (x) + \dots}{1 - \tan (x) + \tan^{2} (x) - \dots + {(- 1)}^{n} \tan^{n} (x) \dots} = 1 + \sin (2 x)$

Casertowm7 2022-02-26

Prove the identity
$1 + \sin x = 2 \cos^{2} (45^{\circ} - \frac{x}{2})$

Phoebe Xiong 2022-02-26

Use the de Moivre theorem to evaluate the following:
$\frac{(1 + i) {(\sqrt{3} + i)}^{3}}{{(1 - \sqrt{3} i)}^{3}} = 1 - i$

Tayyib Cornish 2022-02-26

The equation of motion given is
$x (t) = \frac{- 2}{3} \cos (10 t) + \frac{1}{2} \sin (10 t)$

haugmbd 2022-02-26

I need to prove by induction that:
$\sum_{k = 1}^{n} \sin (k x) = \frac{\sin (\frac{n + 1}{2} x) \sin (\frac{n}{2} x)}{\sin (\frac{x}{2})}$

manhangasto6 2022-02-26

Solve
$2 + \cot θ = \csc θ$
where
$0 \leq θ < 2 π$ ?

Nettie Potts 2022-02-26

What will be the minimum value of
$\frac{p^{2}}{{\tan 90}^{\circ}} + \frac{q^{2}}{{\tan 27}^{\circ}} + \frac{r^{2}}{{\tan 63}^{\circ}} + \frac{s^{2}}{{\tan 81}^{\circ}}$
If
$p + q + r + s = 5$
where p,q,e,s are positive reals?

Layla-Rose Ellison 2022-02-26

Given that x and y satisfy the equation:
$\arctan (x) + \arctan (y) + \arctan (x y) = \frac{11}{12} π$

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