Solving Trigonometry Problems: Basic, Advanced & Examples

High School
Geometry
Trigonometry

Which area is more fundamental: parallelogram or triangle?

poklanima5lqp3 2022-05-09

I have a triangle that I know the lengths of all the sides. But I need to know the angles. Needs to work with non-right triangles as well.
I know it is possible, and I could have easily done this years ago when I was in trig, but it has completely slipped my mind.
I'd prefer a solution that I can code into a function, or something that does not require constructing right triangles from it.

deformere692qr 2022-05-09

Use an expression for $\frac{\sin (5 θ)}{\sin (θ)}$ to find the roots of the equation $x^{4} - 3 x^{2} + 1 = 0$ in trigonometric form

Logan Lamb 2022-05-09

If $α$ , $β$ , $γ$ , $δ$ are smallest positive angle in ascending order of magnitude which have their sines equal to positive quantity $λ$ , then if
$4 \sin \frac{α}{2} + 3 \sin \frac{β}{2} + 2 \sin \frac{γ}{2} + \sin \frac{δ}{2} = 2 \sqrt{1 + λ}$
then $λ$ = ?
Options-
(1) $\sin α$
(2) $\sin β$
(3) $\sin γ$
(4) $\sin δ$

Damion Hardin 2022-05-09

Solve the equation $\frac{1}{(\cos θ)^{2}} = 2 \sqrt{3} \tan θ - 2$

Aedan Gonzales 2022-05-08

How to use trigonometric identities to simplify $\frac{1}{(1 - \csc x) (1 + \csc x)}$ ?

lurtzslikgtgjd 2022-05-08

Let $A$ be the set of all $d$ such that $d < 1$ and $d = \frac{a}{b}$ where $a^{2} + b^{2} = c^{2}$ and $a, b, c \in I$ . Is A an infinite or finite set and how can that be proven?

Ainsley Zimmerman 2022-05-08

Proving the identity $\csc x - \sin x = (\cot x) (\cos x)$

Dominick Blanchard 2022-05-07

The base of a pyramid is a right triangle with the longest side = 12cm. All non base edges are also equal to 12cm. And how can I find the height of the pyramid?

Paul Duran 2022-05-07

Solve the trigonometric series equation $1 + \sin x + \sin^{2} x + \sin^{3} x + \dots = 4 + 2 \sqrt{3}$

Aedan Gonzales 2022-05-07

The equation is
$a \cos (ω t) + b \sin (ω t) = A \cos (ω t + ϕ)$
I must have forgotten how the right hand side follows from the left hand side.
Some hints would be helpful

lnwlf1728112xo85f 2022-05-07

Prove: $\csc a + \cot a = \cot \frac{a}{2}$
All I have right now, from trig identities, is
$\frac{1}{\sin a} + \frac{1}{\tan a} = \frac{1}{\tan (a / 2)}$
Where do I go from there?

Find the volume of the pyramid. Write your answer as a fraction or mixed number.

Julian Peck 2022-04-15

Find $\sin \frac{θ}{2}$ when $\sin θ = \frac{35}{}$ , and $0^{\circ} < θ < 90^{\circ}$
The answer I'm currently getting is $\sqrt{\frac{1}{10}}$ but the answer must be either $\frac{\sqrt{10}}{10}, \frac{3 \sqrt{10}}{10} or \frac{13}{}$
My Process:
since $\sin \frac{θ}{2} = \pm \sqrt{\frac{1 - \cos θ}{2}}$
$\sqrt{\frac{1 - \frac{4}{5}}{2}} \cdot \sqrt{\frac{5}{5}} = \sqrt{\frac{5 - 4}{10}} = \sqrt{\frac{1}{10}}$

Karissa Sosa 2022-04-06

Prove this trigonometry equation: $\sin 40^{\circ} \cdot \sin 50^{\circ}$ is equal to $\frac{1}{2} \cos 10^{\circ}$

Kaiden Wilkins 2022-04-06

Solving an equation with $\sin (x)$ in the exponent: $2^{\sin (x)} \cdot \cos (x) + 1 = 1$

lornjety2o 2022-04-02

Solve: 8 tan^2(alpha)- sen^2(alpha)=tan^2(alpha) sen^2(alpha)

f(t)=sin(2t)

valor.21ict 2022-04-01

Erik Cantu 2022-03-31

I calculated ${\sin 75}^{\circ}$ as $\frac{1}{2 \sqrt{2}} + \frac{\sqrt{3}}{2 \sqrt{2}}$ , but the answer is $\frac{\sqrt{2} + \sqrt{6}}{4}$ . What went wrong?
I calculated the exact value of ${\sin 75}^{\circ}$ as follows:
${\sin 75}^{\circ} = \sin (30^{\circ} + 45^{\circ})$
$= \sin 30 ° \cos 45 ° + \cos 30 ° \sin 45 °$
$= \frac{1}{2} \cdot \frac{1}{\sqrt{2}} + \frac{\sqrt{3}}{2} \cdot \frac{1}{\sqrt{2}}$
$= \frac{1}{2 \sqrt{2}} + \frac{\sqrt{3}}{2 \sqrt{2}}$
The actual answer is
$\frac{\sqrt{2} + \sqrt{6}}{4}$

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Trigonometry

Trigonometry Problems - Basics, Advanced & Examples