Solving Trigonometry Equations and Problems with Examples and Tips

prove that $\sum_{k = 1}^{n = 90} \frac{1}{\sin (k - 1) \sin (k)} = \frac{\cos 1^{\circ}}{\sin^{2} 1^{\circ}}$

Gretchen Schwartz 2022-07-03

Prove $4 \sin (40^{\circ}) - \sqrt{3} = \cot (50^{\circ})$

myntfalskj4 2022-07-02

How does $\int_{π / 3}^{π / 2} \frac{1 - \cos^{2} x}{\sqrt{\sin^{2} (x / 2)}} d x$ simplify to $\int_{π / 3}^{π / 2} 4 \sin (x / 2) \cos^{2} (x / 2) d x$ ?

Kolten Conrad 2022-07-02

Solving $\cos^{2} θ - \sin θ = 1, θ \in [0^{\circ}, 360^{\circ}]$

doturitip9 2022-07-02

Solve this trigonometric equation. $\frac{1}{\sqrt{2}} (\sin (θ) + \cos (θ)) = \frac{1}{\sqrt{2}}$
Divide both sides by $\frac{1}{\sqrt{2}}$
$\sin (θ) + \cos (θ) = 1$
Divide both sides by $\cos (θ)$
tan(θ)+1=sec(θ)
square both sides:
$\tan (θ) + 1 = \sec (θ)$
$\tan^{2} (θ) + 2 \tan (θ) + 1 = \sec^{2} (θ)$
Use the identity $\sec^{2} (θ) = \tan^{2} (θ) + 1$ :
$\tan^{2} (θ) + 2 \tan (θ) + 1 = \tan^{2} (θ) + 1$
$∴$
$2 \tan (θ) = 0$
∴
$\tan (θ) = 0$
∴
$θ = 0, π, 2 π$
I know that 0 and $2 π$ are correct but that $π$ is wrong. I also know that the other correct answer is $\frac{π}{2}$ .

2d3vljtq 2022-07-02

Show that
$\tan 72^{\circ} - \cot 36^{\circ} - \cot 54^{\circ} = 3 \tan 18^{\circ}$

aangenaamyj 2022-07-02

What is the value of the expression $[1 + \cos (\frac{π}{8})] [1 + \cos (\frac{3 π}{8})] [1 + \cos (\frac{5 π}{8})] [1 + \cos (\frac{7 π}{8})]$ ?

Jamison Rios 2022-07-02

Prove trigonometric identity and how to have ideas
This is the identity:
$\cos^{2} (a) - \cos^{2} (b) = \frac{\tan^{2} (b) - \tan^{2} (a)}{(1 + \tan^{2} (a)) \cdot (1 + \tan^{2} (b))}$

Ellen Chang 2022-07-02

Issues computing $\int \cos^{2} x d x$ without using $\sin^{2} (x) = 1 - \cos^{2} (x)$

Holetaug 2022-07-02

How to calculate $\log_{5} \tan (36^{\circ}) + \log_{5} \tan (54^{\circ})$ without a calculator?

Logan Wyatt 2022-07-02

Compute $\sum_{k = 0}^{180} \cos^{2} 2 k^{\circ}$

pablos28spainzd 2022-07-02

If the quadratic equation $x^{2} + (2 - \tan θ) x - (1 + \tan θ) = 0$ has two integral roots,then find the sum of all possible values of $θ$ in interval $(0, 2 π) .$

Crystal Wheeler 2022-07-02

Proof that $a^{\tan x} + a^{\cot x} \leq 2 a$ where $\frac{1}{2} \leq a \leq 1$ and $0 \leq x \leq \frac{π}{4}$

Keenan Santos 2022-07-02

What is
$\sum_{r = 1}^{90} \arctan (\frac{2 r}{2 + r^{2} + r^{4}})$

auto23652im 2022-07-02

Prove that $(2 \sqrt{3} + 4) \sin x + 4 \cos x$ lies between $- 2 (2 + \sqrt{5})$ and $2 (2 + \sqrt{5})$

delirija7z 2022-07-02

If $\cos α, \cos β, \cos γ$ are the roots of $9 x^{3} - 9 x^{2} - x + 1 = 0,$ , Then $α + β + γ$

woowheedr 2022-07-01

Showing that $x \cos φ + y \sin φ < 2$

myntfalskj4 2022-07-01

$\cot (2 \cot^{- 1} t)$ simplifies to?

cdsommegolfzp 2022-07-01

Show that in a $Δ A B C$ , $\sin \frac{A}{2} \leq \frac{a}{b + c}$
Hence or otherwise show that $\csc^{n} \frac{A}{2} + \csc^{n} \frac{B}{2} + \csc^{n} \frac{C}{2}$ has the minimum value ${3.2}^{n}$ for all $n \geq 1$

lilmoore11p8 2022-07-01

Solving $\int \frac{2 \sin (x) \cos (x)}{\sin^{4} (x) + \cos^{4} (x)} d x$

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