0
votes
1answer
13 views

Find catesian coordinate of T-point $P(-\frac{65\pi}{2}) $

Find the Cartesian coordinates of T-point $P(-\frac{65\pi}{2}) $. It is easy when there is no negative sign. I don' t know how to do with negative sign.
1
vote
2answers
22 views

Finding Principale period of $\cos$ function

Find principle period of $3\cos (2x-3)$. Today I have learned about principle period of various trigonometric function. I know that principle period of cos is $2 \pi$. Please someone can help me ...
2
votes
3answers
40 views

Prove that $\frac{\tan^2\theta(\csc\theta-1)}{1+\cos\theta}=\frac{(1-\cos\theta)\csc^2\theta}{\csc\theta+1}$

Question: $$\frac{\tan^2\theta(\csc\theta-1)}{1+\cos\theta}=\frac{(1-\cos\theta)\csc^2\theta}{\csc\theta+1}$$ Prove that L.H.S.=R.H.S. My Efforts: ...
1
vote
1answer
31 views

Find the value of $27\csc^2\theta+8\sec^2\theta$

$10\sin^4\theta+15\cos^4\theta=6$, then find the value of $27\csc^2\theta+8\sec^2\theta$ I don't know how to do it have just tried by converting sin and cos into csc and sec. But can't get the ...
1
vote
3answers
34 views

Trigonometric Proof:

Question: If $m\cos\alpha-n\sin\alpha=p$ then prove that $m\sin\alpha+n\cos\alpha=\pm \sqrt{m^2+n^2-p^2}$ My Efforts: $(m\cos\alpha-n\sin\alpha)^{2}=p^2$ ...
1
vote
3answers
81 views

Trigonometric proof [L.H.S.=R.H.S]

Question: $$\frac{2-3\sin\theta+\sin^3\theta}{\sin\theta+2}=2\sin\theta (\sin\theta-1)+\cos^2\theta$$ I don't know how to start with these problem. Normally these type of proof confuse me. In my ...
4
votes
3answers
46 views

Trigonometric identity, simplifying an expression to $(1-\sin^2 a\cos^2a)/(2+\sin^2a\cos^2a)$

Question: $$\left(\frac{1}{\sec^2A-\cos^2A}+\frac{1}{\csc^2A -\sin^2A}\right)\sin^2A\cos^2A=\frac{1-\sin^2A \cos^2A}{2+\sin^2A\ \cos^2A}$$ Prove L.H.S. = R.H.S. My Efforts: ...
2
votes
3answers
53 views

Why $ (1- \sin \alpha + \cos \alpha)^2 = 2 (1 - \sin \alpha)(1+ \cos \alpha)$?

Why $ (1- \sin \alpha + \cos \alpha)^2 = 2 (1 - \sin \alpha)(1+ \cos \alpha)$? I am learning trigonometric identities one identity I have to proof is the next: $ (1- \sin \alpha + \cos \alpha)^2 = ...
1
vote
5answers
72 views

Prove $\frac{\sin A}{\sec A+\tan A-1}+ \frac{\cos A}{\csc A+\cot A-1}=1$

$$\frac{\sin A}{\sec A+\tan A-1}+ \frac{\cos A}{\csc A+\cot A-1}=1$$ Prove that L.H.S.$=$R.H.S. This type of questions always creates problem when in right hand side some trigonometry function is ...
0
votes
3answers
149 views

Derivatives of sine and cosine at $x=0$ give all values of $\frac{d}{dx}\sin x$ and $\frac{d}{dx}\cos x$?

In video 3 of the video lectures by MIT on Single Variable Calculus presented by David Jerison, the latter says: Remarks: $\dfrac{d}{dx}\cos x\left|\right._{x=0}=\lim\limits_{\Delta ...
1
vote
1answer
67 views

How to show that the triangle is equilateral triangle?

If $\cot A+\cot B+\cot C=\sqrt3$ then prove that the triangle is equilateral triangle. Trial: I can counter check that this is true as $\cot 60+\cot 60+\cot 60=3 \frac{1}{\sqrt3}=\sqrt3$.Here I ...
6
votes
3answers
180 views

How can I find all the solutions of $\sin^5x+\cos^3x=1$

Find all the solutions of $$\sin^5x+\cos^3x=1$$ Trial:$x=0$ is a solution of this equation. How can I find other solutions (if any). Please help.
7
votes
2answers
90 views

How to show this inequality?

Show that $$-2 \le \cos \theta(\sin \theta+\sqrt{\sin^2 \theta +3})\le2$$ Trial: I know that $-\dfrac 1 2 \le \cos \theta\cdot\sin \theta \le \dfrac 1 2$ and $\sqrt 3\le\sqrt{\sin^2 \theta ...
4
votes
4answers
1k views

Learning trigonometry on my own.

I have been self teaching myself math beginning with a grade 10 level for a while now and need learn trigonometry from near scratch. I am seeking both books and perhaps lectures on trigonometry and ...
9
votes
3answers
362 views

Being ready to study calculus

Some background: I have a degree in computer science, but the math was limited and this was 10 years ago. High school was way before that. A year ago I relearnt algebra (factoring, solving linear ...
3
votes
2answers
99 views

Please, help me to find where is a mistake in the solutions of the equation.

I have this equation and I will be very thankful to anyone who can provide me any help with the one discrepancy in my solution and the solution from the self-learning website: $$ \frac{1+\tan(x) + ...
4
votes
1answer
115 views

Is it allowed to divide an equation by an expression which can be equal to zero?

I need a help in such a problem and will greatly appreciate any suggestions. I was taught, division of an equation by an expression which can be equal to zero can lead to missing roots. But I thought ...
6
votes
2answers
115 views

Missing and parasite roots in the trigonometric equation.

I have this equation: $$\boxed{\cos(2x) - \cos(8x) + \cos(6x) = 1}$$ RIGHT And its right solution from the textbook is: $$ \begin{align} \cos(2x)+\cos(6x)&=1+\cos(8x)\\\\ ...
3
votes
2answers
90 views

Conditions for Moving Function Outside Sine Argument

Are there multiple discrete functions $f[n]$ such that \begin{align} \sin \left( f[n] x[n] \right) = f[n] \sin \left( x[n] \right) \end{align} I know that the above equation holds for $f[n] = 0$, ...
2
votes
2answers
328 views

Good SAT learning resources?

I'm looking to brush up on SAT math. (That's basic algebra, probability and trigonometry.) I'm interested in books and websites.
6
votes
4answers
721 views

What are some good resources for brushing up on geometry and trigonometry?

I'm brushing up on my calculus, and geometry and trigonometry keep coming up. However, these are probably my weakest areas mathematically. Are there any good sites or free PDFs/ebooks that I can use ...