Solving Trigonometry Equations and Problems with Examples and Tips

Difference between $\frac{2 π}{b}$ versus $2 π b$
I'm having trouble finding period involving this equation: $y = a \sin (x - h b) + k$ . Sometimes my teacher would use $\frac{2 π}{b}$ in order to solve for period and sometimes my teacher would use $2 π b$ to solve for b. What is the difference between the two equations, and how do I know which one is the appropriate equation to use in a problem.

David Rodgers 2022-03-27

Converting parametric to cartesian - $x = 4 \cos t$ and $y = 4 \sin t$ as $x^{2} + y^{2} = 16$

Ashleigh Shaffer 2022-03-27

Consider the function
$f (x) = \sin x + \cos x + \tan x + \cot x + \sec x + \csc x$
Let P be the smallest possible positive real number such that the equation f(x)=P has real solutions, and let N be the largest possible negative real number such that the equation f(x)=N has real solutions.
Find the value of $[1000 (P + N)]$

burubukuamaw 2022-03-27

Computing $\int_{0}^{1} \sin (3 π x) \sin (2 π x) d x$

Samara Richard 2022-03-27

Compute $\int \frac{x^{2}}{\tan {x} - x} d x$ for $x \in (0, \frac{π}{2})$

xxgetthisar08 2022-03-27

How do I go about simplifying $1 - \frac{\sin^{2} x \tan x}{\tan x + 1} - \frac{\cos^{2} x}{\tan x + 1}$ to $\sin x \cos x$

Deegan Chase 2022-03-27

How do I compute the following integral
$I = \int {(\tan x)}^{\frac{1}{6}} d x$

Zack Mora 2022-03-27

How can I simplify
$\sqrt{3^{2} + 3^{2} \tan^{2} θ}$

abitinomaq1 2022-03-27

How can I simplify $\cos (2 x) + \frac{1}{2} \sin (4 x) - \frac{1}{2} \cos (4 x)$ into a single expression?

Harold Hoover 2022-03-27

How can I solve the following inequality:
$6 \sin x \cos 2 x \geq 0$

Petrolovujhm 2022-03-27

Help with exact value of:
$\tan (\sin^{- 1} (- \frac{1}{2}) - \tan^{- 1} (\frac{3}{4}))$

Zack Mora 2022-03-27

Hints to prove $\tan^{2} {θ} = \tan {A} \tan {B}$ ,given $\frac{\sin {(θ + A)}}{\sin {(θ + B)}} = \sqrt{\frac{\sin {2 A}}{\sin {2 B}}}$

Rowan Callahan 2022-03-27

Help solving trigonometric equation $\cos^{2} x - \sin x = 0$ within the domain $[0, 2 π]$

fsrlaihq55 2022-03-27

Help me to find the value of $\frac{\sin^{3} (θ) - \cos^{3} (θ)}{\sin (θ - \frac{π}{4})}$ if $\sin (2 θ) = 2 \sqrt{2} - 2$

Erik Cantu 2022-03-26

Could you please help me prove this:
$\frac{2 \cos (\frac{θ}{2}) - 1 - \cos θ}{2 \cos (\frac{θ}{2}) + 1 + \cos θ} = \frac{1 - \cos (\frac{θ}{2})}{1 + \cos (\frac{θ}{2})}$

Dominique Pace 2022-03-26

Compute the value of
$\frac{(\arctan \frac{1}{2} + \arctan \frac{1}{3})}{(arcot \frac{1}{2} + arcot \frac{1}{3})}$

anadyrskia0g5 2022-03-26

How do I find dx/dt implicitly with the function $\tan (x) = 4 t^{- 1}$ ?

meli199939f 2022-03-26

How do I expand $\sin^{5} θ$ using the complex exponential, in order to obtain:
$\frac{1}{16} \sin 5 θ - \frac{5}{16} \sin 3 θ + \frac{5}{8} \sin θ$

Kiara Haas 2022-03-26

How do I change $\csc x + \cot x$ into $\frac{1}{\csc x - \cot x}$ ?

burubukuamaw 2022-03-26

How can one prove the following equation?
$\sin (9^{\circ}) \sin (27^{\circ}) \sin (63^{\circ}) \sin (81^{\circ}) = \frac{1}{16}$

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