Solving Trigonometry Equations and Problems with Examples and Tips

Show that a function of the form
$x (t) = K_{1} \cos β t + K_{2} \sin β t$
Can be written as
$x (t) = K \cos (B t - ϕ)$
Where $K = \sqrt{K_{1}^{2} + K_{2}^{2}}$
I know that linear systems with complex coefficients are sometimes expressed in this form, however I'm not sure if/how that would be useful to solve this problem.

Quarrippesspevmo 2022-06-02

If $\tan (α) + \cot (α) = a (a > 0),$ , find $\sqrt{\tan (α)} + \sqrt{\cot (α)}$

Lesly Weiss 2022-06-01

$lim_{i \mapsto \infty} \sum_{i = 1}^{\infty} \sin (θ_{i + 1} - θ_{i})$ = ? , where $θ_{i} = π \sum_{j = 0}^{i} \frac{1}{{(2)}^{j}}$

NastreteMutvh5j0 2022-06-01

How do I find all solutions to $\cos (x)^{4} - \sin (x)^{4} = 1$

CorRoorgofmq2b 2022-06-01

Additivity of $\arctan (\frac{x + y}{1 - x y})$

Martin Nunez 2022-06-01

How to prove the trigonometric identity $\frac{1 - \sin φ}{1 + \sin φ} = (\sec φ - \tan φ)^{2}$

Jamison Estrada 2022-06-01

If $a, b, c \in R^{+}$ and $\frac{1}{a + 1}$ + $\frac{1}{b + 1}$ + $\frac{1}{c + 1}$ = 2, then $\sqrt{a b}$ + $\sqrt{b c}$ + $\sqrt{a c}$ $\leq$ $\frac{3}{2}$

Trevor Wood 2022-05-31

Verify that $\frac{1}{\tan (x) \csc (x)} = \cos (x)$

patzeriap0 2022-05-31

Find the value of $(\tan 35 ° + \tan 55 °) (\sin 35 ° + \sin 55 ° + 1) (\cos 35 ° + \cos 55 ° + 1)$

Kenley Wagner 2022-05-31

Find out the general solution of $\tan x + \cot 2 x = 2$

kunyatia33 2022-05-31

find minimum value of $2^{\sin^{2} (θ)} + 2^{\cos^{2} (θ)}$

Nicholas Cruz 2022-05-31

How to simplify $\sqrt{\sin 2 a} + \sin a$

Brennen Fisher 2022-05-31

Proving $\frac{\sin (120^{\circ})}{1 + \sin (90^{\circ} + a)} - \frac{\sin (240^{\circ})}{1 - \cos (- a)} = \frac{\sqrt{3}}{\sin^{2} (a)}$

prensistath 2022-05-30

How to prove the divergence of the following sum: $\sum_{x = 1}^{\infty} \cot^{- 1} [\frac{1}{1 + x^{2} + x}]$

realburitv4 2022-05-30

How to prove this trig identity turning tan into cot?
$\frac{\tan u - \tan v}{1 + \tan u \cdot \tan v} = \frac{\cot v - \cot u}{\cot u \cdot \cot v + 1}$

Jaycee Mathis 2022-05-30

I found the following formula here: Taylor Series of $\tan x$ .
Taylor series of $\tan x$ :
$\tan x = \sum_{n = 1}^{\infty} \frac{(- 1)^{n - 1} 2^{2 n} (2^{2 n} - 1) B_{2 n}}{(2 n)!} x^{2 n - 1}$

Landyn Jimenez 2022-05-30

Proving the irrationality of the number $\cos \frac{π}{9}$

Nasir Kim 2022-05-29

Show that $r e^{i θ} = s e^{i α} ⟹ r = s and θ = α + 2 π k$ and $r e^{i θ} = s e^{i α} ⟹ r = s and θ = α + 2 π k$

Serena Carpenter 2022-05-29

Find the period of $2 \sin (2 x) \cos^{2} (x)$

Charity Daniels 2022-05-29

How do I convert to only cos?
$y = \cos (t) - \sin (t) \to y = A \cos (ω t - ϕ)$

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