Trigonometric equation Definition and 133 Threads

Hello reader, I have an exam really soon and it includes a good bit of trigonometry, but I'm having problems with the trig stuff because this exam does not allow calculators and since I was dependent on the calculator, I haven't memorized anything about the trigonometric functions. I don't know...

Can anyone help with this trig question, Determine the smallest angle in degrees such that sin theta+5cos theta=4 Iknow i need to use the quadratic formula but really stuck on it.

Homework Statement 4sec2θ tanθ = 8 tanθ Homework Equations sec2θ = tan2θ + 1 The Attempt at a Solution 4(tan2 + 1) tanθ = 8 tanθ (4tan2 + 4) tanθ = 8 tanθ 4 tan3 + 4 tanθ = 8 tanθ 4 tan3 - 4 tanθ = 0 4tanθ(tan2θ - 1) = 0 4tanθ = 0 tanθ = 0 tan-1(tanθ) = tan-1(0) tan-1θ = 0, π tan2θ - 1 = 0...

Find the value of x between 0 degrees and 360 degree satisfying the equation 10sin^2x+ 10sin x cos x - cos^2x = 2 this is how i have attempted..... 10 sin^x+ 10sin2x/2 - cos^x = 2 I used the property sin 2x = 2 sin x cos x and substituted sin x cos x with sin 2x/2 giving me.... 11sin^2x +...

Solve the equation $\sin^6 a+\cos^6 a=0.25$.

a) Solve the trigonometric equation: A = cosX + AsinX, for some angle X. b) The imaginary number i is equal to √-1. Use part a) to solve i = cosX + isinX. You will have used degrees to answer parts a) and b). However, the mathematics below requires the use of radians. Convert degrees to...

Is correct the following procediment? ## A \sin (\omega t) = A \sin (\phi) \to \phi= \sin^{-1} \sin (\omega t )## Is correct to say that ## \phi = \omega t## is oscillatory in this case ??

Homework Statement 4sin2(2x) -1 = 0 Solve over 0 --> 2pi The attempt at a solution (2sin(2x) + 1) (2sin(2x) - 1) = 0 2sin(2x) +1 = 0 sin(2x) = -1/2 2x = -pi/6 x = -pi/12 and -11pi/12 which = 23pi/12 and 13pi/12. 2sin(2x) - 1 = 0 sin(2x) = 1/2 2x = pi/6 x= pi/12 and...

Here is the question: I have posted a link there to this thread so the OP can view my work.

Show that the trigonometric equation $\sin (\cos a)= \cos (\sin a)$ has no solutions.

Let $y$ be in radians and $0<y<\dfrac{\pi}{4}$. Solve for $y $ if $\tan 4y=\dfrac{\cos y-\sin y}{\cos y +\sin y}$.

$2\cos{\theta}+2\sin{\theta}=\sqrt{6}$ $\displaystyle\cos{\theta}+\sin{\theta}=\frac{ \sqrt{6} }{2}$ $\displaystyle(\cos{\theta}+\sin{\theta})^2=\frac{3}{2}$ $\displaystyle\cos^2{\theta}+2cos\theta\sin\theta+\sin{\theta}^2=\frac{3}{2}$ $\displaystyle\sin{2\theta}=\frac{1}{2} \Rightarrow...

Homework Statement 2 sin(2x) = 2 cos(x) Homework Equations The Attempt at a Solution 4sinxcosx-2cosx=0 2(2sinxcosx-cosx)=0 2cosx(sinx-1)=0 2cosx=0 sinx=1 And then I did the math and got pi/2 and 3pi/2 , but that's apparently wrong.

Homework Statement Solve: 2 tan x (tan x - 1) = 3. Homework Equations Pythagorean identities? The Attempt at a Solution I tried the following: 2 tan^2 x - 2 tan x = 3 2 (sec^2 x - 1) - 2 tan x = 3 2 (1 - cos^2 x) - 2 sin x cos x = 3 cos^2 x (multiplying through by cos^2 x)...

Solve the equation $$\sqrt{3}\sin x(\cos x-\sin x)+(2-\sqrt{6})\cos x+2\sin x+\sqrt{3}-2\sqrt{2}=0$$

Here is the question: I have posted a link there to this topic so the OP can see my work.

Solve $$\sqrt{2}\cos \left(\frac{x}{5}-\frac{\pi}{12} \right)-\sqrt{6}\sin \left(\frac{x}{5}-\frac{\pi}{12} \right)=2\left(\sin \left(\frac{x}{5}-\frac{2\pi}{3} \right)-\sin \left(\frac{3x}{5}+\frac{\pi}{6} \right) \right)$$

Solve the equation $$\cos^2 \left(\frac{\pi}{4}(\sin x+\sqrt{2}\cos^2 x)\right)-\tan^2 \left(x+\frac{\pi}{4}\tan^2 x\right)=1$$

Homework Statement cos 2x + cos 4x = cos x 0 degrees ≤ X ≤ 360 degrees Homework Equations Trig identities. The Attempt at a Solution Trig identities and equations are my weakness so I'm trying to review some to get better at them, so I guess this isn't technically homework...

Here is the question: Here is a link to the question: PRE-CALC QUESTION!? HELP !? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Here is the question: Here is a link to the question: Help with trig equation :)? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Here is Katie's question: Here is a link to the original question: Solve for x in the equation 1+sinx/cosx + cosx/1+sinx = 4 for 0 < x < 2pi? - Yahoo! Answers I'll post a link there to this topic so the OP can find my response.

I want to prove this equation: \cos\left(\frac{2\pi}{5}\right)+\cos\left( \frac{4\pi}{5}\right)+\cos\left( \frac{6\pi}{5}\right)+\cos\left(\frac{8\pi}{5} \right) = -1 . I've no idea how to begin. I think it may be related to complex numerd but I don't know how to combine them.

Homework Statement Solve cot^{-1} x - cot^{-1} (n^2 - x+1)=cot^-1(n-1) Homework Equations The Attempt at a Solution I can write the above equation as θ+α=β where the symbols represent the respective inverse functions. Now I take tan of both sides. Simplifying I get...

Homework Statement Solve 2cos(x)^2 + 3cos(x) + 1 = 0 for 0 <= x <= 2pi Homework Equations Trigonometric equations, yadda yadda yadda. The Attempt at a Solution 2cos(x)^2 + 3cos(x) + 1 = 0 cos(x)(2cos(x) + 3) = -1 cos(x) = -1/(2cos(x) + 3) I then figured out that you get a solution when...

2Cos (3/10x) - 3Sin(1/2x)=0 How would I go about solving this equation? I do not even know where to begin.

Hi, may you help me? I have a question I solved but couldn't ended. If cos(x)+5Sec(x)=1.1 then Cos(x)=? 2Cos(x)+5Sec(x) =11/10 2Cos(x)+5/Cos(x)=11/10 2Cos(x)*Cos(x)+5=11/10*Cos(x) 2Cos^2(x)+5=11/10*Cos(x) 2Cos^2(x)-11/10-Cos(x)-5=0 then i used delta=b^2-4ac then i found delta=-4.79...

solve for tan^4x + tan^2x = sec ^4x - sec^2x i solved and ended up with RIHS= tan^4x?

I have this as part of a calculus problem. I guess I am a little rusty on this. Any help would be appreciated. 4\cos^2{x}=\frac{\sec^2{x}}{4} I believe that I need to solve for cosx. And then determine what cosx is in radians. That should be the lower limit of the integration. I know how it...

Hello everyone! Homework Statement Solving a relatively general equation representing a constant combination of 2 trigonometric functions.Homework Equations a\cos{(vx+p)}+b\cos{(ux+q)}=cThe Attempt at a Solution I really don't have any idea for a general solution to this equation.. Best Regards

Homework Statement All solutions in the interval 0 ≤ x < 2∏ Sin 2x = -2cos x The Attempt at a Solution I went about it in two different ways. The first way: I simply used the double angle formula to get 2sinx cosx + 2cos x = 0 From this we get that whatever makes cos x = 0...

Homework Statement A beach ball is riding the the waves near Tofino, BC. The ball goes up and down with the waves according to the formula h= 1.4 sin(∏t/3), where h is the height in meters above sea level, and t is the time in seconds. A) In the first 10s when is the ball @ sea level. B)...

Homework Statement Given y = 2/3(arctan \frac{x}{4}), find x. Homework Equations Inverse trigonometric identities for tan. (I guess)The Attempt at a Solution I never attempted because it seems impossible for me. You think this is possible? Thank you!

EDIT: 1.Homework Statement The problem asks to simplify this: cos(arcsin x)Homework Equations let arc sin x = θThe Attempt at a Solution EDIT: I have to edit because I received a warning for not posting for #3 and #2. I originally posted "cos(arcsin x)" for #2 because that was what I know...

Number of real solution of the equation $\sin (\sin (\sin x)) = \cos (\cos (\cos x))$ where $ 0 \leq x\leq 2\pi$

can somebody help me out on this one,i got stuck on this one https://www.physicsforums.com/attachments/164

Homework Statement tan(\alpha)=\sqrt{2}-1 for every alpha in ]0,90°[ Homework Equations 1-count tan(2α) 2-conclude the value of α The Attempt at a Solution 1-after using tan(2α)=(2tanα)/1-tan^2α) i got tan(2α)=(√2-1)/2 2- I know that α is pi/8 but i just don't know how to...

Homework Statement cos 2x-cos^2 x=0 The Attempt at a Solution I have no idea.

Hi, thank you for looking. Homework Statement Solve the following complex equation and carefully plot at least 3 solutions for each. State ALL solutions to each! State exact answers! Sin(z)=√(3) The Attempt at a Solution Here is my work. I was a little confused how to tell what...

Hi, I wolud like to solve the folowing equation: A*cos(B*t)+sin(B*t)*(C-t)-D=0 (t is unknown) It is urgent. Thanks in advance. Regards Mike

Homework Statement a. find the tangent and normal line at P (0,0) b. find when the tangent is horizontal Equation: 3x+sin3x at (0,0) The Attempt at a Solution Find the derivative- y'=3 (?) or it it 3x+cos(3x)? But from there, I don't know how to find the rate of change to create a...

Homework Statement This is a question from my test paper. If sec \theta=\frac{4xy}{(x+y)^2}, where x,y \in R, then (a)x,y \in R+ (b)x,y \in R- (c)x=y\neq0 (d)x\inR+, y\inR- Homework Equations The Attempt at a Solution I don't understand what i have to do and where should...

Having Trouble: Solving a Trigonometric Equation using Identities ? Homework Statement I am having problems with these. Need some help please! Here is a sample question I am having troubles with: 3 cos θ + 3 = 2 sin^2 θ, 0 <= θ < 2pi I am really struggling with these. Any help...

Fx = sin [ 90 - theta ] * [ dX - [tan (theta) * dY ] ] ??

Homework Statement I took a test in my Precalculus class about 3 weeks ago, and the tests were handed back this week. I saw that I didn't do so well because I was stumped on this equation: 3[FONT="Georgia"]sinx + 4[FONT="Georgia"]cosx = 1 Homework Equations We were to use the following...

Homework Statement Find all solutions to the following equation: sin((5*x/2)+15)=0.433 where 0 < x < 360 Homework Equations The Attempt at a Solution i can find the first value of x that satisfies this equation. (5*x/2)+15=sin^-1(0.433) 5*x/2=10.6581 5*x=21.2162 x=4.2632...

Homework Statement Tan \Theta = 12 / 5, sin\Theta<0Homework Equations Sin ^{2} \Theta+ Cos ^{2}\Theta = 1 The Attempt at a Solution Sin is less than 0 so... it should be somwhere in the II or III quadrant? What identities should I use to solve?

Solve for \theta 20= 32[sin\theta] (72/32[cos\theta]) + 1/2(-9.8){(72/32[cos\theta]}2I'm really having trouble with this question. I've tried it many times, but keep getting stuck. Is there anyway to let X=72/32[cos\theta] and then solve for x with the quadratic equation? Can someone help me...

This is a problem from a quiz I had awhile ago, I got the answer correct, but I'm reviewing for a test and I completely forget how I did it. Can someone please show me what I did? sec4x=2 secx=2 x=π/3 + 2nπ ---> x=π/12+2nπ/4 x=5π/3 + 2nπ ---> x=5π/12+2nπ/4 π=pi p.s. I mostly just forget how...

Homework Statement Which of the following is not a possible solution of 0=sinθ+cosθtan^2θ? A. 3pi/4 B. 7pi/4 C. 2pi D. 5pi/2 Homework Equations All trigonometric identities. The Attempt at a Solution Too much to write down, at least two pages long, but I've been trying to...