# trigonometry

1. ### Prove the cosine rule using vectors

Yr 12 Specialist Mathematics: Triangle ABC where (these are vectors): AB = a BC = b CA = c such that a + b = -c Prove the cosine rule, |c|2= |a|2 + |b|2 -2 |a|.|b| cosB using vectors So far, I've been able to derive |c|2= |a|2 + |b|2 +2 |a|.|b| cosB, with a positive not a negative. I used...
2. ### different answers for derivative?

different answers for derivative?(Solved) Take this trigonometric function: \frac{d \(sin{(\cos{\theta})})^2}{d \theta}} Using the chain rule i think it becomes: -2\theta\sin{(\cos{\theta})}\sin{\theta} But if we use the identity: \sin^2{\theta} = 1-\cos^2{\theta} then the...
3. ### Find the arc length problem inquiry

Hello, I'm studying for my pre-cal exam tomorrow and I'm not sure about a question... Find the length of an arc of a circle radius 8m if the arc subtends a central angle of 1 rad. I multiplied 1 rad by pi, and reasoned that Pi= 180 degrees Then I followed the formula, S= R*theta...
4. ### C3 Trigonometry Question

Here is a question, I've got an answer to it but I think its wrong a) prove that (done) b) verify that is a solution to the equation Does this rearrange to, using part (a), so, , which is correct?? c) Using your result in part (a), or otherwise, find the other two solutions, , of...
5. ### Trigonometry question

Hi, I need help to derivate the following equation : Arc tan (square(x-1)/x) I can't get the correct answer which is : (2-x)/2(x^2+x-1) square (x-1) Here is what I've done so far : du/a^2+u^2 so : du = 1/2square(x-1) a^2 = x^2 u^2 = (x-1) which give me : 1/2(x^2+x-1) square (x-1) can't...
6. ### How should I solve this Trigonometric equation?

For math homework I have to solve the following equation. I know what the answer is, I just don't quite understand how to get there. Can you please help me? So the equation is: sin(2x - ⅓π) = -cos(x + ⅓π) This is how I've solved it so far: sin(2x - ⅓π) = -cos(x + ⅓π) sin(2x - ⅓π) = cos(x +...
7. ### Help with the Trigonometry Equation please!

Hi guys, I am stressing myself out coz i dont know how to do this question. Question being: 2cos(x-30)=1 0o≤X≤360o​ I think you start by dividing both sides by 2 to get: cos(x-30)=1/2, but dont know what you do from here! Thanks in advance Dan ps. could you please explain the working so I...
8. ### Trigonometry Online Course

Hello Everyone, I come to ask a basic question, and I hope I'm not hated for the "stupidness" it involves. The course is an online trigonometry course. Every week I have to do a set of assignments and quiz. I can usually figure out very easily how to complete the assignments since I'm reading...
9. ### Simplify trig equation using identities

So I need to simplify a problem down to ten characters, and I got this far and now I'm stuck: 2cos3t(3sint-4sin3t) +1 I don't really know what to do with the 2cos3t... I feel like distributing it in would just make the problem even messier... Here's the original problem...
10. ### show by algebraic means the value of sin^4(15) - cos^4(15_

i know they are difference of squares but i dont know what to do after....the answer is -root3over2

Can anyone answer the following 3 questions? And state quadrant? (1) Sin 186 (2) tan 150 (3) cos(-65)
12. ### Finding the Exact Value of an Inverse Trigonometry Function

Hello, I want to find the exact value of csc(-\frac{5\pi}{3}) I know that csc(\theta)=\frac{1}{sin(\theta)}, and the answer to the question is \frac{2\sqrt{3}}{3} , but don't know how this works! Thank you for your answers!
13. ### Law of Sines

The bearing from the Pine Knob fire tower to the Colt Station fire tower is N 65 degrees East, and the two towers are 30 km apart. A fire spotted by rangers in each tower has a bearing of N 80 degrees East from Pine Knob and S 70 degrees E from Colt Station. Find the distance of the fire from...

1. Tw0 ships leave a d0ck, The sl0wer ship leaves at n00n, and the 0ther at 1p.m. 0ne sails n0rtheast at the rate 0f 8.5 miles an h0ur, the 0ther sails n0rth at the rate 0f 10 miles an h0ur.H0w far apart are they at 2p.m.?? (can u please give me the figure 0f this please)[case 3 using c0sine law...
15. ### Bearing and Trigonometry

A party of geographers is out on a field trip. They start walking from a church on a bearing of 223 degrees and walk in that direction for 3.5km to get to a lake. They then turn roughly east and walk on a bearing of 101 degrees. After walking for 6.6km it starts to rain heavily and they decide...
16. ### Photogrammetric coordinate geometry

G-Day Maths forum I’m having some trouble with photogrammetric coordinate geometry. I need to know whether it possible to calculate the physical length and angle of an elongated object in 3D space (say a girder hanging from a crane) using the visual length and angle derived from one or more...
17. ### How Do I Find X and Y If Hypotenuse is Given (Trigonometry)

Find the length of Y, to the nearest tenth. I have no idea how to find!! Help please :)
18. ### Reviewing on Trigonometry

Just wondering, I was a bit confused on some trigonometry problems when they have a number along with the theta. For example, what if you have a problem like this: 2csc2Ɵ-8cscƟ+8=1 This is what I did: 1. 2csc2Ɵ-8cscƟ+7=0 Then it looked like a quadratic formula to me. So I set it up, and in the...
19. ### Trig Equations

Solve for 0<x<2 7sin2x-11 = 4sin2x-13 7sin2x-11-4sin2x+13=0 sin2x = -2/3 How can I solve it further, giving the answer in exact form?(Thinking)(Thinking)