Solving Trigonometry Equations and Problems with Examples and Tips

How can I solve $cosh (z) = 2$ for $z \in C$ ? My steps have only led to values of z which are not imaginary, those being $\ln (2 + \sqrt{3})$ and $\ln (2 - \sqrt{3})$ . How do I find solutions to the equations that are imaginary?

mwombenizhjb 2022-03-26

How can I prove $| \tan (x) + \tan (y) | \geq | x + y |$ with the Mean Value Theorem?
for all $x, y \in [- \frac{π}{2}, \frac{π}{2}]$

Oxinailelpels3t14 2022-03-26

Given that $5 \sin x - 12 \cos x = 13 \sin (x - 67.4)$
Find the maximum value of $5 \sin x - 12 \cos x + 1$ and the corresponding value of x from 0 to 360.
Maximum value = 13+1=14
Corresponding value of x
$13 \sin (x - 67.4) + 1 = 14$
$\sin (x - 67.4) = 1$
$x = 157.4, 337.4$
I found the value of x and there’s 2 values. However , the answer is only157.4 why is that the case ?

Arianna Villegas 2022-03-25

Determining derivatives of trigonometric functions
$lim_{x \to \frac{π}{4}} \frac{\tan x - 1}{4 x - π}$
the value of f'(a)?

ashes86047xhz 2022-03-25

Definite integral
$\int_{1}^{\frac{π}{8}} (x - 1) \sin 4 x d x$

jisu61hbke 2022-03-25

Computing $\int_{0}^{π} \frac{d x}{1 + a^{2} \cos^{2} (x)}$

Harley Ayers 2022-03-25

Computing $\int_{0}^{\frac{π}{2}} \frac{1}{4 \cos {x} + 5}, x \in R$ by substituting $\cos {x} = \frac{e^{i x} + e^{- i x}}{2}$ ?

Addison Fuller 2022-03-25

Compute $lim_{x \to \frac{π}{2}} \frac{(1 - \sin x) (1 - \sin^{2} x) \dots (1 - \sin^{n} x)}{\cos^{2 n} x}$

Kiara Haas 2022-03-25

How do I get from
$\frac{\sqrt{3}}{2} + \frac{1}{2} \tan x - 2 \tan x \cdot \frac{\sqrt{3}}{2}$
to
$\frac{\sqrt{3}}{2 \sqrt{3} - 1} = \tan x$
and then to
$11 \tan x = 6 + \sqrt{3}$

Amya Horn 2022-03-25

How can one simplify
$\arctan (\frac{1}{\tan α})$

Kiara Haas 2022-03-25

Given:
$\frac{1 - \cos (x) + k \sin (x)}{\sin (x) + k + k \cos (x)}$

acidizihvzs 2022-03-25

Given,
$\cos \frac{x}{2} + \sin (3 x) + \sqrt{3} (\sin \frac{x}{2} + \cos (3 x))$

Overath097p 2022-03-25

Given that:
$2 \cos (x + 50) = \sin (x + 40)$
Show, without using a calculator, that:
$\tan x = \frac{1}{3} \tan 40$

Kiara Haas 2022-03-25

Given that $\sin A = \frac{4}{5}, \cos (A + B) = \frac{5}{13}$ and that A and B are acute, find $\cos B$

tibukooinm 2022-03-25

For which values a, the equation
$a \sin x + (a + 1) \sin^{2} \frac{x}{2} + (a - 1) \cos^{2} \frac{x}{2} = 1$

Makayla Stevens 2022-03-25

Would someone recommend a method of proving this relation?
$| e^{- 2 x} \sin (x) | \leq \frac{x}{1 + x^{2}}, x \geq 0$
Unfortunately differentiation leads to messy transcendental expressions.

Landen Barber 2022-03-25

Which is bigger $\tan^{- 1} (\frac{1}{2})$ or $\frac{1}{\sqrt{5}}$ ?

Jackson Floyd 2022-03-25

Given $3 \cos x - 4 \sin x = 2$ find $3 \sin x + 4 \cos x$ without first solving for x

encaderpwp 2022-03-25

Given an angle $θ$ , the formulas for $\sin (\frac{θ}{2})$ and $\cos (\frac{θ}{2})$ are either positive or negative, which is why $\pm$ is used in their formulas. So, if $\tan (\frac{θ}{2}) = \frac{\sin (\frac{θ}{2})}{\cos (\frac{θ}{2})}$ , and both the numerator and denominator are either positive or negative (and unless $θ$ is defined, we must assume they can be both), shouldn't the formula for $\tan (\frac{θ}{2})$ also be $\pm$ ?
Below are the equations I am referring to.
$\sin (\frac{u}{2}) = \pm \sqrt{\frac{1 - \cos (u)}{2}}$
$\cos (\frac{u}{2}) = \pm \sqrt{\frac{1 + \cos (u)}{2}}$
$\tan (\frac{u}{2}) = \frac{1 - \cos (u)}{\sin (u)} = \frac{\sin (u)}{1 + \cos (u)}$

Lesnaoq73 2022-03-25

General solution of $(\sqrt{3} - 1) \sin θ + (\sqrt{3} + 1) \cos θ = 2$

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