Trigonometric Functions

Solve the equation -6cos(𝝅t/6)+10 ≥ 12 for t.For context: The equation models a harbour on a certain day, in which y≥12 represents where it is safe for a ship to enter or leave the harbour. I need to...

BACKROUND INFO: (Answer from question a)Tidal waves such as the one below do not really follow a normal trigonometric graph of the form $y= k cos at+ c$ So the behaviour of the data instead that preve...

The graph of 𝑦 = 3cos(2(𝑥 +12°)) - 5 is the same as the graph of 𝑦 = 3sin(2(𝑥 +G°)) -5. State 2 values of G. Show steps.

Hello,I would really appreciate some help understanding the derivation for x' and y' for Equation (1), Equation (2), and Equation (3). I recall that to convert Cylindrical Coordinates to Cartesian Coo...

Please help solve the questions in the photos. 

I have an object that I need to rotate/reposition. I want to use a rotation matrix but because the x,y position of the object is determined by 6 values ( lets say x = 435, 435, 510 and y= 500 ,456, 54...

Hello!Here is a trig problem I simply do not have the knowledge to solve, please help! Here are the rules:TASK: Create a complex or simple polygon with the smallest possible perimeter adhering the fol...

My instructor told us that the integral of square root of tangent can be evaluated. How can one really do it? 

Find the colume of the solid obtained by rotating the graph of the function $y=\sin x$ around $x$-axis between $x=0$ and $x=\pi$.

Compute \lim\limits_{x \rightarrow 0} \frac{1-\frac{1}{2}x^2-\cos(\frac{x}{1-x^2})}{x^4}

5. (a) For the triangle, a=10, b=12, B=60°, labelled by convention, find all the angles and sides. (b) Solve the following, 𝑠𝑖𝑛𝜗−𝑐𝑜𝑡^2𝜗=1, express your solution in degrees in the range –180°≤𝜗≤180°, a...

In the figure below you will see a "flower" with a green leaf limited by a closed simple curve, calculate the area of the curve: r(t)=(cos(5t)-cos(7t),sin(5t)+sin(7t)),for $t\in (0,\pi/6)$. You can us...

Prove that $tan x +cot x=sec x  csc x$. Please show all the required work. 

Hello all, I'm hoping someone can help me with this issue I've been having for a few days: I have this function in Desmos: https://www.desmos.com/calculator/h2owg1no4t If you parse through the inputs,...

Show that $\sum_{n=1}^{\infty} \frac{\sin n}{n}$ is convergent. I was trying to use the Dirichlet test, but couldn't verify that the conditions of the Dirichlet test are satisfied. 

Attached is a photo of the problem. Help would be much appreciated. It involves proving an identity using t-formulas, then using that result prove the following using mathematical induction. Then, sho...

Is the infinite series \sum_{i=1}^{\infty}\arctan (\frac{n+1}{n^2+5}) convergent or divergent?

Find the average of $f(x)=\sin x$ on $[0, \pi]$.

Is $\sum_{n=1}^{\infty}\frac{\arctan (n!)}{n^2}$ convergent or divergent?Which test should I use? I feel so dumb! 

Evaluate $\int \sin x \sqrt{1+\cos x} dx$. Please show work, thanks. 

Find the area under the graph of $y=\sin x$ between $x=0$ and $x=\pi$.

Determine whether the following integral is convergent or divergent. Justify your answer.\int_0^1 \frac{\cos x}{x \sin^2 x}dx

Find the average value of the function f(x)=\frac{\sin x}{1+\cos^2 x}on the interval $[0,1]$.

I am tired of trying to evaluate \int x^2(1-x^2)^{-\frac{3}{2}}dx.I am substituting $x=\sin \theta$, but get stuck in the remaining calculations. A detailed answer would be greatly appreciated. 

Evaluate $\int \sqrt{\tan x} dx$