Solving Trigonometry Equations and Problems with Examples and Tips

Resolve $A = \cos (π / 7) + \cos (3 π / 7) + \cos (5 π / 7)$ using $u = A + i B$

veneciasp 2022-07-01

Substitute $x = a \sin θ$ into $\frac{a x^{2}}{\sqrt{a^{2} - x^{2}}}$ and simplify
So when i substituted, i got the following:
$\frac{a * a^{2} \sin^{2} θ}{\sqrt{a^{2} - a^{2} \sin^{2} θ}}$

Patatiniuh 2022-07-01

Let $z = \cos x + i \sin x$ . Show that
$1 + z = 2 \cos \frac{1}{2} x (\cos \frac{1}{2} x + i \sin \frac{1}{2} x)$

Bruno Pittman 2022-07-01

To prove that $\tan 70 = \tan 20 + 2 \tan 50$

babyagelesszj 2022-07-01

If $A + B + C = \frac{π}{2}$ thrn prove that:
$\tan (A + B) [\tan A - \tan B] = \sqrt{1 + \cot^{2} C} (\sec A \cos B - \cos A \sec B)$

Cooper Doyle 2022-07-01

If
$\tan (\frac{π}{12} - x), \tan (\frac{π}{12}), \tan (\frac{π}{12} + x)$
in order are three consecutive terms of a GP then what is sum of all possible values of x.
I am not getting any start, can anybody provide me a hint?

Wade Bullock 2022-07-01

Proving $\int_{0}^{1} \frac{\sin π x}{x^{2} + 1} d x = \frac{2}{π (μ_{1}^{2} + 1)} = \frac{π}{4} \sin π μ_{2}$ for certain $μ_{1}, μ_{2} \in [0, 1]$

Jameson Lucero 2022-07-01

If $a, b, c \in (0, \frac{π}{2}),$ , Then prove that $\frac{\sin (a + b + c)}{\sin a + \sin b + \sin c} < 1$

Wade Bullock 2022-07-01

The following equation
$\sin (x + \frac{π}{4}) = \sin (\frac{3}{8} π - 3 x)$

Leland Morrow 2022-07-01

$If \sqrt{9 - 8 \sin 50^{\circ}} = a + b \csc 50^{\circ}, then a b = ?$

minwaardekn 2022-07-01

Finding convergence/abs convergence/divergence of series with trig function
$\sum_{n = 1}^{\infty} \frac{\sin (4 n)}{4^{n}}$

Dania Mueller 2022-07-01

I have been trying to simplify this expression:
$\cos (θ) - \frac{1}{\cos (θ) + i \sin (θ)}$

Brunton39 2022-07-01

Why isn't $\arctan θ = \frac{\arcsin θ}{\arccos θ}$ ?

pouzdrotf 2022-06-30

Prove $\sin^{2} θ + \cos^{4} θ = \cos^{2} θ + \sin^{4} θ$

vasorasy8 2022-06-30

If $x e^{9 y} + y^{4} \sin (4 x) = e^{8 x}$ implicitly defines y as a function of x then what is $\frac{d y}{d x}$ ?

Cierra Castillo 2022-06-30

If $A + B + C + D = 2 π$ , prove that: $\cos A + \cos B + \cos C + \cos D = 4 \cos \frac{A + B}{2} \cdot \cos \frac{A + C}{2} \cdot \cos \frac{B + C}{2}$

pipantasi4 2022-06-30

Solving $a \sin x + b \cos x = c$
Suppose $a \sin x + b \cos x = c$ . My teacher told me that with changing variable we can solve it by this : $(c + b) t^{2} - 2 a t + (c - b) = 0$ where $t = \tan \frac{x}{2}$ . I thought it is true always but today found a problem . When we define $\sin x$ and $\cos x$ with $\tan \frac{x}{2}$ , we should consider $\cos \frac{x}{2} \neq 0$ and $x \neq 2 k π + π$ but it can be the answer of the main equation (i.e. $a \sin x + b \cos x = c$ ) ! So , that formula is incomplete ?

Jovany Clayton 2022-06-30

For any triangle ABC with sides a,b,c prove that
$a \cos A + b \cos B + c \cos C \leq \frac{a + b + c}{2}$
How to initiate this question?

Rapsinincke 2022-06-30

Find the exact value of $\cot ({202.5}^{\circ})$

sweetymoeyz 2022-06-30

Rewriting $\sin (a + b) = c$

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