Solving Trigonometry Equations and Problems with Examples and Tips

Prove that $\sin \frac{π}{14}$ is a root of $8 x^{3} - 4 x^{2} - 4 x + 1 = 0$

palmantkf4u 2022-03-31

Rewrite $f (x) = 3 \sin (π x) + 3 \sqrt{3} + 3 \sqrt{3} \cos (π x)$ in the form $f (x) = A \sin (K x + D)$

Alexis Alexander 2022-03-31

Prove that $\frac{\sin 5 x}{\sin x} \in (- \frac{5}{4}, 5)$ for any $x \in R k π$ where $k \in Z$ .

tibukooinm 2022-03-31

Prove that $cosh (x) = \sec (θ)$ if $x = \ln (\sec θ + \tan θ)$

Blackettyl2j 2022-03-31

Prove that $\cos x \cdot \cos \sqrt{3} x = 1$ has exactly one solution at x=0

Averie Ferguson 2022-03-31

prove that maximum value of $\cos α \cos β$ occurs when $α = β = \frac{σ}{2}$
If $α, β \in (0, \frac{π}{2})$ and $α + β = σ$ (constant), then prove that maximum value of $\cos α \cos β$ occurs when $α = β = \frac{σ}{2}$

Sage Fry 2022-03-31

Prove that
$\sin (12^{\circ}) \sin (48^{\circ}) \sin (54^{\circ}) = \frac{1}{8}$

Alfredo Holmes 2022-03-31

Prove that
$\cos^{2} (θ) + \cos^{2} (θ + 120^{\circ}) + \cos^{2} (θ - 120^{\circ}) = \frac{3}{2}$

encaderpwp 2022-03-31

Prove that
$\sin (\frac{π}{3} + x) = \cos (\frac{π}{6} - x)$

calcolare45pj 2022-03-31

Prove that
$\int_{0}^{π} \frac{\cos x \cos 4 x}{{(2 - \cos x)}^{2}} d x = \frac{π}{9} (2160 - 1247 \sqrt{3})$

Zoie Phillips 2022-03-31

Prove that
$\frac{1}{90} \sum_{n = 1}^{90} 2 n \cdot \sin ({(2 n)}^{\circ}) = \cot (1^{\circ})$

michiiiiiakqm 2022-03-31

Prove that
$(\sin^{2} \frac{x}{2}) \cdot \frac{\sqrt[3]{4}}{3} \cdot {\frac{1}{\sin x + 1 - x}}^{\frac{2}{3}}} < 1$

Anika Boyd 2022-03-31

Prove $\sin 8 θ - \sin 10 θ = \cot 9 θ (\cos 10 θ - \cos 8 θ)$

Nadia Clayton 2022-03-31

Prove $\frac{\cos (x)}{1 - \tan (x)} + \frac{\sin (x)}{1 - \cot (x)} = \sin (x) + \cos (x)$

aanvarendbq28 2022-03-31

Prove ${[\cos (θ + \frac{π}{3}) + i \sin (θ + \frac{π}{3})]}^{6} = \cos (6 θ) + i \sin (6 θ)$

Pizzadililehz 2022-03-31

Prove $(1 + \sec x) (1 + \csc x) > 5$ if $x \in [0, \frac{π}{2}]$ .

markush35q 2022-03-31

Prove
$\sin (5 θ) = 16 \sin^{5} (θ) - 20 \sin^{3} (θ) + 5 \sin (θ)$

Jasmine Todd 2022-03-31

Proof that
$2 \sin (1.5 x) \cos (1.5 x) = 3 \sin (x) - 4 \sin^{3} (x)$

acidizihvzs 2022-03-31

Proof of trig identity using t-formulae
Show that
$2 \arctan x = \arccos \frac{1 - x^{2}}{1 + x^{2}}$
if x>0, and
$2 \arctan x = - \arccos \frac{1 - x^{2}}{1 + x^{2}}$
if x<0.
I have been able to equate the expressions by letting $x = \tan (\frac{y}{2})$ , but I do not know how to show the different signs of the equation for x>0 and x<0.

David Rodgers 2022-03-31

Proof of $\cos α + \sin β + \cos γ = 4 \cdot \sin (\frac{α}{2} + 45 °) \cdot \sin \frac{β}{2} \cdot \sin (\frac{γ}{2} + 45 °)$
I tried to simplify right side:
$4 (- \frac{1}{2} (\cos (\frac{α}{2} + \frac{γ}{2} + \frac{π}{2}) - \cos (\frac{α}{2} - \frac{γ}{2})) \cdot \sin (\frac{β}{2}) =$
$= - 2 \cdot \sin (β) \cdot \cos (\frac{α}{2} + \frac{γ}{2} + \frac{π}{2}) + 2 \cos (\frac{α}{2} - \frac{γ}{2}) \cdot \sin (\frac{β}{2}) =$
$= - \sin (\frac{β}{2} + \frac{α}{2} + \frac{γ}{2} + \frac{π}{2}) - \sin (\frac{β}{2} - \frac{α}{2} - \frac{γ}{2} - \frac{π}{2}) + \sin (\frac{β}{2} + \frac{α}{2} - \frac{γ}{2}) + \sin (\frac{β}{2} - \frac{α}{2} + \frac{γ}{2})$

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