Precalculus Solutions | Expert Assistance for Problems & Examples

What is $\tan α$ if $\sin α + \cos α = \frac{\sqrt{3} - 1}{2}$ and $α \in (90^{\circ}, 135^{\circ})$

Porter Mccullough 2022-04-19

The function f is defined, for $x \geq 0$ , by $f (x) = 4 - 3 \cos (\frac{x}{2})$
Given that $f (n a + b) = 2.5$ where a is positive constant and n=0,1,2,..., find the smallest possible value of b and least value of a.

juniorychichoa70 2022-04-19

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

Jaylyn Villarreal 2022-04-18

We have to find all real solutions to this system of equations:
$x = \frac{4 z^{2}}{1 + 4 z^{2}}, y = \frac{4 x^{2}}{1 + 4 x^{2}}, z = \frac{4 y^{2}}{1 + 4 y^{2}}$

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?
$\cos^{6} (2 x) + \sin^{6} (2 x) = \frac{5}{8}$

Kale Bright 2022-04-17

How do I solve for x algebraically?
$\frac{x^{2} (x^{2} - 1)}{x + 3} = 12$

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 $\sqrt{3} - \sqrt{2}$

Precalculus problems and solutions are hard to find online even though this topic is quite popular among college students majoring in Engineering. Keeping this fact in mind, we decided to provide you with a list of questions and answers that will help you with various precalculus problems. Regardless if it is related to equations or any other problem, these precalculus problems and composite functions examples and solutions below will help you see the logic and compare solutions as you check your original task.

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