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Trigonometry Questions
From the top, K of a building 320 m high, the angles of depression of the top, L and bottom, M of another building on th…
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Use trigonometric ratios to find the size of the angle marked θ and β in each of the following right-angled triangles.
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Find the value of the unknown sides in each of the following right angled triangles. Use trigonometric ratios to find th…
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Determine the value of lengths y and z. Determine the value of the following. Show all calculations sin a sin2 a + cos2…
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Evaluate the following integrals: I. ∫(6t⁴+4t³−t²+1)dt II. ∫(3x²−6x−2)dx. Evaluate the following by method of substituti…
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A person is standing 18 m away from a water tank. The angle of elevation from the person's eye level to the top of the t…
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A plane is flying at an altitude of 5km. From the plane, the angle of depression to airport A and airport B are 45 and 3…
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Let sin 22° = p. Determine the following ratios in terms of p: 2.2.1 sin 202°, 2.2.2 cos 44°
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If 25 sin θ = -7 and 0° < θ < 270°, determine with the aid of a diagram, the values of the following: 1.1 tan θ 1.2 sec…
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The diagram below shows the graphs of f(x) = 2sin 2x and g(x) = a tan bx. Give the coordinates of A and B. Write down th…
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From the diagram, Find the value of 1) Sin x, Cos x and tan x ii) Sin x - Cos x iii) (Sin x + tan x)", Solve
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y = (t2 sin t) / (cos t). 2) If y = (t2 sin t) / (cos t) show that t2(d2y/dt2) + 4t(dy/dt) - (t2+6)y = 0. 3) If y = tn s…
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Trigonometry: Solving the right angled triangle. SOHCAHTOA. Solve problems 4, 5 and 6.
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In the diagram, /PQ/ = 8 m, /QR/ = 13 m, the bearing of Q from P is 050° and the bearing of R from Q is 130°. Calculate…
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tan(45-30) = (tan 45 - tan 30) / (1+tan 45.tan 30) = (1-1/sqrt(3))/(1+1.1/sqrt(3))
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Triangle KLM is similar to triangle LRS where angle K corresponds to angle Q and where angles L and R are right angles.…
View SolutionAbout 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
Label opposite, adjacent and hypotenuse on the diagram before choosing a ratio. The ratio then chooses itself.
For bearings, always draw the north arrow at the point you are measuring from. Nearly every bearing error is a missing north line.
Check the mode on your calculator before the first keystroke. A whole page of correct method scores nothing in the wrong mode.
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.
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Message Us on WhatsAppFrequently 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 priority support.
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 & Articles
What Is the Pythagorean Theorem? Formula, Proof & Examples
Learn the Pythagorean theorem with clear examples and proofs. Understand a² + b² = c² and how to use it to find missing sides of right triangles.
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Learn 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.
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