Solving Trigonometry Equations and Problems with Examples and Tips

Solve:
$3 \sin x - \cos x)^{4} + 6 {(\sin x + \cos x)}^{2} + 4 (\sin^{6} x + \cos^{6} x)$

Porter Mccullough 2022-04-19

Solve:
${(\sin \frac{π}{8} + \cos \frac{π}{8})}^{2}$

Jakayla Benton 2022-04-19

Solve $\sin 7 x + \sin 3 x = 0$

Perla Benitez 2022-04-18

What approach would be ideal in finding $\frac{d^{40} y}{{d x}^{40}}$ , when $y = \sin x$ ?

Delilah Novak 2022-04-18

How do I solve this equation:
$\sin x - 3 \sin 2 x + \sin 3 x = \cos x - 3 \cos 2 x + \cos 3 x$

Delilah Novak 2022-04-18

How do I simplify a radical within a radical in this half-angle problem?
$\sin (- \frac{3 π}{8}) = \pm \sqrt{\frac{1 + \frac{\sqrt{2}}{2}}{2}}$

Justine White 2022-04-18

How do I solve
$\int 4 \cos^{2} (x) d x$

Alivia Rojas 2022-04-18

How do i solve
$\sin (8 x) - \cos (6 x) = \sqrt{3} (\sin (6 x) + \sin (8 x))$

Breanna Mcclure 2022-04-17

What is $\arctan (x) + \arctan (y)$ if $x y = 1$

Bryanna Leon 2022-04-17

How do you evaluate
$lim_{x \to 0} \frac{2 - \cos (3 x) - \cos (4 x)}{x}$ ?

Haylee Bowen 2022-04-17

How do you establish the trigonometric identity?
$\frac{{(2 \cos^{2} θ - 1)}^{2}}{\cos^{4} θ - \sin^{4} θ} = 1 - 2 \sin^{2} θ$

Lillianna Sandoval 2022-04-17

How do I solve the following equation for x?
$\cos^{6} (2 x) + \sin^{6} (2 x) = \frac{5}{8}$

Destinee Bryan 2022-04-16

Let ABC be an acute triangle. What is the maximum value of
$\frac{\tan^{2} A + \tan^{2} B}{\tan^{4} A + \tan^{4} B} + \frac{\tan^{2} B + \tan^{2} C}{\tan^{4} B + \tan^{4} C} + \frac{\tan^{2} C + \tan^{2} A}{\tan^{4} C + \tan^{4} A} ?$
For the equilateral triangle, $\tan A = \tan B = \tan C = \sqrt{3}$ , and the sum is 1. For the isosceles triangle with $∠ A = ∠ B \to \frac{π}{2}$ and $∠ C \to 0$ , the sum approaches zero.

Aliana Alvarez 2022-04-16

knowing: $\tan x = 2 - \sqrt{3}$ , obtain: $\cos 2 x$
I tried converting $\tan x$ into it's sinus and cosine form and trying to square both sides to try to get the form of:
$\cos^{2} x - \sin^{2} x$
But I can't really get to this form without having extra expressions of sine or cosine, any ideas how to start this properly?
Taken out of one of the entry tests to Maths in TAU.
Solution:
$\cos 2 x = \cos^{2} x - \sin^{2} x = \frac{\cos^{2} x - \sin^{2} x}{\sin^{2} x + \cos^{2} x} : \frac{\cos^{2} x}{\cos^{2} x} = \frac{1 - \tan^{2} x}{1 + \tan^{2} x}$
$\frac{1 - \tan^{2} x}{1 + \tan^{2} x} = \frac{- 6 + 4 \sqrt{3}}{8 - 4 \sqrt{3}} = \frac{- 3 + 2 \sqrt{3}}{4 - 2 \sqrt{3}}$

Brooks Barker 2022-04-16

Is there nice radical expression for
$\cos (\frac{π}{2^{k} + 1})$

Annie Rice 2022-04-16

Is $\arccos (\frac{\sqrt{6} + 1}{2 \sqrt{3}}) = \arctan (\frac{\sqrt{3} - \sqrt{2}}{1 + \sqrt{6}})$ ?
They are equal according to the calculator but how?
I made a triangle with base $\sqrt{6} + 1$ and hypotenuse $2 \sqrt{3}$
Then the height comes out to be $\sqrt{5 - 2 \sqrt{6}}$ using Pythagoras theorem.
But it should come out to be $\sqrt{3} - \sqrt{2}$

Emmy Decker 2022-04-16

Is $\sin (ω t + π) = - \sin ω t$ always true no matter what $ω$ is?
For example, it's true that $\sin (t + π) = - \sin (t)$ . You flip one over the x-axis, and you get the other. But $\sin (2 t + π) = \sin (2 t)$ . Because $\sin (2 t)$ has a period of $π$ , so if you translate it by π, you are still gonna get $\sin (2 t)$

Mina Whitehead 2022-04-16

What is $\arctan (- \tan (θ))$ equal to?

Papierskiix5n 2022-04-16

What is a bound of $\frac{1}{\sin x} - \frac{1}{x}$ on $(0, a]$ ?
Is $\frac{1}{\sin x} - \frac{1}{x}$ bounded in $(0, a]$ , $a < \frac{π}{2}$ ?

Aiyana Ayers 2022-04-16

How do I solve this equation $R$ :
$3 \sin^{3} x + 2 \cos^{3} x = 2 \sin x + \cos x$

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