Practice Trigonometric Functions Problems

High School
Geometry
Trigonometry
Trigonometric Functions

Recent questions in Trigonometric Functions

Alonzo Odom 2022-08-01

Find the exact value.
$\tan (6 π)$

Bernard Boyer 2022-07-27

$h (t) = \cot (t)$
[(3.14)/(4), ((3)(3.14)/(4))]
Find the average rate of change of the function over the given interval or intervals.

Libby Owens 2022-07-27

t is a real number and P=(x,y) is the point on the unit circlethar corresponds to t. Find the exact values of the six trigonometric functions of t.
$(\frac{1}{2}, \frac{- \sqrt{3}}{2})$

Darryl English 2022-07-25

the solid lies between planes perpendicular to the x-axis at x=-1 and x=1. the cross-sections perpendicular to the x-axisare
a. circles whose diameters stretch from the curve $y = - \frac{1}{\sqrt{1 + x^{2}}}$ to the curve $y = \frac{1}{\sqrt{1 + x^{2}}}$
b. vertical squares whose base edges run along the same ends

Nelson Jennings 2022-07-25

Show that f is continuous on $(- \infty, \infty)$ .
$f (x) = {\begin{cases} \sin (x) i f x < π / 4 \\ \cos (x) i f x \geq π / 4 \end{cases}$

f(t)=sin(2t)

assume a,b starts on the positive x-axis and moves around in a circle. determine a function of a segment from the origin to a point a,b

Let $S_{n} = \sum_{j = 1}^{n} \sin (\sqrt{j} π)$ .

Show $S_{(2 M)^{2}} < 0$ and $S_{(2 M + 1)^{2}} > 0 (M = 1, 2, 3, . . .)$ .

kejpsy 2022-01-26

Find coordinate points where the tangent line is horizontal for $f (x) = - \sin (8 x) + 6 \cos (4 x) - 8 x$

Tessa Leach 2022-01-25

Find modulus and argument of $ω = \frac{\sin (P + Q) + i (1 - \cos (P + Q))}{(\cos P + \cos Q) + i (\sin P - \sin Q)}$

pozicijombx 2022-01-25

Given that $\tan \frac{x}{2} = \frac{1 - \cos (x)}{\sin (x)}$ , deduce that $\tan \frac{π}{12} = 2 - \sqrt{3}$
I know $\tan \frac{x}{2} = \frac{1 - \cos (x)}{\sin (x)}$ is true and I can prove it by squaring and taking a square root of the right side then I multiply by $\frac{0.5}{0.5}$ . And I will use
$\cos \frac{x}{2} = \sqrt{\frac{1 + \cos x}{2}}$
and
$\sin \frac{x}{2} = \sqrt{\frac{1 - \cos x}{2}}$
But I do not understand the part of deducing.

stropa0u 2022-01-24

If $y = \arctan (\frac{2 x - 1}{1 + x - x^{2}})$ , then $\frac{d y}{d x}$ at x=1 is equal to?
I have tried 2 different approaches, both yielding different results and both results are present in the options. Am I doing something wrong or why is this happening?

Jazmin Perry 2022-01-24

If $g (x) = f (\tan^{2} x - 2 \tan x + 4), 0 < x < \frac{π}{2}$ , then g(x) is increasing in what interval?
I have first differentiated the given equation and found the value of x for which the interior part of f is 3 ,this gives $x = \frac{π}{4}$ and it gives me $g (\frac{π}{4}) = 0$ but I am stuck here and don't know what to do after this.

Maximus George 2022-01-24

Find the maximum angle X in the range $0^{\circ} \leq x \leq 360^{\circ}$ which satisfies the equation $\cos^{2} (2 x) + \sqrt{3} \sin (2 x) - \frac{74}{=} 0$

Tori Hines 2022-01-24

Why must x be acute for the identity $\sqrt{\frac{1 - \sin x}{1 + \sin x}} = \sec x - \tan x$ to hold true?

poveli1e 2022-01-24

If $\cos 2 v = - \frac{19}{}$ and v is acute, then determine the value of v
I have tried using the double angle identity
$\cos 2 v = \cos^{2} v - \sin^{2} v$
Ive

Nataly Best 2022-01-23

How do you find $\sin (\sin^{- 1} (\frac{1}{4}))$ ?

Adrien Barron 2022-01-23

Determine the greatest possible value of
$\sum_{i = 1}^{10} \cos 3 x_{i}$
for real numbers $x_{1}, x_{2} \dots x_{10}$ satisfying
$\sum_{i = 0}^{10} {\cos x}_{i} = 0$
My attempt:
$\sum \cos 3 x = \sum 4 \cos^{3} x - \sum 3 \cos x = 4 \sum \cos^{3} x$
So now we have to maximize sum of cubes of ten numbers when their sum is zero and each lie in interval [−1,1]. i often use AM GM inequalities but here are 10 numbers and they are not even positive. Need help to how to visualize and approach these kinds of questions.

poveli1e 2022-01-23

How can you calculate $\arctan (2) + \arctan (3)$ 's value?

bistandsq 2022-01-23

How do you evaluate $\sec [\cot^{- 1} (- 6)]$ ?

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