Trigonometry Homework Help
Step-by-step AI solutions. Ask your own question
Trigonometry questions
- Show that if y = (1 + Cos(2x)) / Sin(2x), then dy/dx = −2[1 + Cos(2x)] / Sin²(2x)
- Given that sin θ = 4/5 and tan θ < 0. Determine with the aid of a diagram and WITHOUT the use of a calculator: 5.1.1 tan…
- Solve the equation cos x = sin 2x, in the interval 0 <= x <= pi. Express 5 cos x − 12 sin x in the form Rcos(x + a)…
- Given that f(θ) = (cos θ / (1-tan θ)) + (sin θ / (1-cot θ)). (a) Prove that f(θ) ≡ cos θ + sin θ. (b) Express f(θ) in…
- Express 208'x - 3 sin(x) in the form R cos(x + α).
- The diagram shows a semi-circle APB with AB as diameter. The midpoint of AB is O. The point P on the semi-circle is such…
- On the grid provided, draw the graph of y = 50x. Daudi was standing on a balcony. He observed a ball on the ground, 47 m…
- A ship travels 100 km on a bearing of 045°, then turns to a bearing of 120° and travels 180 km to its destination. (i)…
- Show that sin(2 arc sin x) = 2x / (7−4x²)
- Use the iterative formula xn+1 = sin⁰¹(2/(xn+2)) with initial value x¹ = 0.75, to determine this root correct to 2…
- Prove the identity (sinx + cosx)(1-sinxcosx) = sin³x + cos³x.
- Using the approximations sinx≈x and cos x ≈ 1- 2 2, where x is small and measured in radians, show that 1- cos 2x sinx…
- Using the approximations sin x ≈ x and cos x ≈ 1 − x²/2, where x is small and measured in radians, show that (1 - cos…
- Express cos6θ in terms of powers of cosθ using De Moivre's Theorem.
- Express 4 cos θ – 3 sin θ in the form R sin(θ – α), where R > 0 and 0° < α < 360°, giving α to the nearest degree. Solve…
- Hence solve (1-cos 2x)/(sin 2x)+3 cos x=2 sin x, for 0°<x<360°. Give your answers correct to 1 decimal place.
- The bearing of B from A is 245, what is the bearing of A from B?
- What are the various rules involved when differentiating or integrating . How do we integrate or differentiate…
About Trigonometry
Trigonometry connects angles to lengths, and once that connection is clear it turns a surprising number of practical problems — heights, distances, bearings, journeys at sea — into a triangle with one side missing. The questions here are largely right-angled triangle work, the sine and cosine rules, angles of elevation and depression, bearings, and identities to prove.
Popular topics in Trigonometry
Right-Angled Triangles
Sine, cosine and tangent ratios, SOHCAHTOA, finding a side or an angle, and Pythagoras alongside them.
Sine & Cosine Rules
Solving non-right-angled triangles, the ambiguous case, and the area of a triangle as ½ab sin C.
Angles of Elevation & Depression
Heights of buildings, trees and cliffs, and the two-station problems that need a pair of equations.
Bearings
Three-figure bearings, back bearings, and multi-leg journeys solved with the cosine rule.
Trigonometric Identities
The Pythagorean identities, compound and double angle formulae, and proving an identity by working one side.
Trigonometric Equations
Solving within a given range, the general solution, and using the quadrants to find every valid angle.
Graphs of Trig Functions
The shapes of sin, cos and tan, amplitude and period, and transformations such as y = a sin bx.
Radians & Arcs
Converting between degrees and radians, arc length, sector area, and small-angle work.
How ScanSolve helps with Trigonometry
ScanSolve labels the triangle before it calculates: which side is opposite, which is adjacent, where the right angle is, and which ratio therefore applies. For bearings it draws the north line at each point, which is the step that makes a "bearing of Q from P" question straightforward rather than confusing.
Solutions state whether the calculator should be in degrees or radians, keep exact values where a question asks for them, and for equations list every solution inside the given range instead of the first one. Identity proofs are shown one side at a time, so the logic reads as a proof rather than a rearrangement.
Study tips for Trigonometry
- 01
Label opposite, adjacent and hypotenuse on the diagram before choosing a ratio. The ratio then chooses itself.
- 02
For bearings, always draw the north arrow at the point you are measuring from. Nearly every bearing error is a missing north line.
- 03
Check the mode on your calculator before the first keystroke. A whole page of correct method scores nothing in the wrong mode.
- 04
When a question asks for all solutions in a range, sketch the graph or use the quadrants. The calculator only ever gives you one of them.
Frequently asked Trigonometry questions
How can ScanSolve help with Trigonometry homework?
ScanSolve's AI solves trigonometry problems step by step. Snap a photo of your homework or type your question to get instant, detailed solutions with clear explanations.
Is Trigonometry homework help free on ScanSolve?
Yes, ScanSolve offers free trigonometry homework help with step-by-step solutions. Upgrade to Pro at $89.99/year (about $7.50/month) or $9.99/week for unlimited answers and our most capable AI model.
What Trigonometry topics does ScanSolve cover?
ScanSolve covers all trigonometry topics including Right-Angled Triangles, Sine & Cosine Rules, Angles of Elevation & Depression, Bearings, Trigonometric Identities. Upload any trigonometry problem and get a step-by-step solution.
Can ScanSolve solve trigonometry problems from a photo?
Yes. Take a photo of your trigonometry homework and ScanSolve's AI will read the problem, identify the method needed, and provide a complete step-by-step solution.
How accurate are ScanSolve's trigonometry solutions?
ScanSolve uses advanced AI to deliver accurate, step-by-step trigonometry solutions. Each answer includes detailed explanations so you can verify the reasoning and learn the method.
Trigonometry study guides
All articles- What Is the Pythagorean Theorem? Formula, Proof & ExamplesLearn the Pythagorean theorem with clear examples and proofs. Understand a² + b² = c² and how to use it to find missing sides of right triangles.
- How to Find the Area of a Triangle: Formulas, Heron's Formula & ExamplesLearn how to find the area of a triangle using base and height, Heron's formula, and trigonometry. Step-by-step examples and practice problems for geometry students.
- Free Mathway Alternative — Unlimited AI Math Solver Without SubscriptionFind the best free Mathway alternative with step-by-step solutions. ScanSolve gives you unlimited math solving with full explanations — no $9.99/mo subscription.
More in Maths
Explore more subjects
Have a Trigonometry question?
Get a step-by-step solution in seconds. Or send a photo of your trigonometry homework on WhatsApp — no app download needed.