Trigonometry Online Center
Trigonometry Math: Free Practice Test, Lessons & Worksheets
If trig has felt like a pile of disconnected formulas, start here. We will build it gently: first triangles, then the unit circle, then identities, equations, graphs, and real applications.
See the idea first
Look at the picture before the formula. Strong math starts when the symbols match something you can see.
Try a few questions first, then open the lesson that matches the mistake.
No need to read everything at once. Start with a small check-in, notice the part that feels shaky, and study that one skill with focus.
Start with the ratios
Name opposite, adjacent, and hypotenuse first. Then sine, cosine, and tangent stop feeling like guesses.
Make the unit circle friendly
Practice exact values, reference angles, and quadrant signs until the pattern feels familiar.
Use identities with purpose
Turn identities into small moves for rewriting, simplifying, and solving instead of memorizing a list.
Solve equations carefully
Find every answer in the interval and check that each angle really works.
Read the graph like a story
Look for amplitude, period, shifts, reflections, and asymptotes before doing any heavy calculation.
Connect trig to real problems
Use triangle laws, sector formulas, and area formulas when the picture is not a right triangle.
Pick the lesson you need today
Use this as your study map. The order moves from foundations to mixed problem solving, but you can also jump straight to the skill that is blocking you right now.
41 guided lessons and tools
Foundations and right-triangle trig
Identities, equations, and inverses
Graphs and transformations
- Graph the Sine Function
- Graph the Cosine Function
- Amplitude, Period, and Phase Shift
- Write the Equation of a Sine Graph
- Write the Equation of a Cosine Graph
- Graph the Tangent Function
- Graph the Cosecant Function
- Graph the Secant Function
- Graph the Cotangent Function
- Sketch Trigonometric Graphs
- Domain and Range of Trigonometric Functions
Formulas with meaning
Do not rush this section. Read one formula, say what it measures in plain English, then work one example where that formula actually helps.
sin(theta)=opp/hyp, cos(theta)=adj/hyp, tan(theta)=opp/adjBefore using it, say what the formula is measuring and what each symbol means.
sin^2(theta)+cos^2(theta)=1Before using it, say what the formula is measuring and what each symbol means.
tan(theta)=sin(theta)/cos(theta)Before using it, say what the formula is measuring and what each symbol means.
csc=1/sin, sec=1/cos, cot=1/tanBefore using it, say what the formula is measuring and what each symbol means.
a/sin(A)=b/sin(B)=c/sin(C)Before using it, say what the formula is measuring and what each symbol means.
c^2=a^2+b^2-2ab cos(C)Before using it, say what the formula is measuring and what each symbol means.
Helpful tools when you get stuck
Use these after you try a problem on your own. They are best for checking steps, seeing a pattern again, or building a longer review plan.
Trigonometry Calculator
Use this when a triangle or trig value feels stuck and you want to compare your setup with the guided steps.
Unit Circle Calculator
Check exact values and angle positions, then pause and notice the pattern before moving on.
Law of Sines and Cosines Calculator
Use this when the triangle is not right and you need a calm way to find a missing side or angle.
Ultimate Trigonometry Course
Open this when you want a broader worksheet-and-review path after practicing the focused skills here.
Common mistakes we can fix early
Mixing up the ratio
Slow down and label the sides from the marked angle. Once the labels are right, the ratio is usually obvious.
Forgetting quadrant signs
A unit-circle value is not only a number. Its sign comes from where the terminal side lands.
Stopping after one angle
Trig equations often have more than one solution in the interval. After the first answer, ask where the same value appears again.
Graphing without the parent shape
Sketch the parent curve first. Then apply amplitude, period, shift, and reflection one change at a time.
A practical study plan
If time is short, do not try to read every lesson in one sitting. Use a check-in first, then spend your energy on the weakest skill.
Review SOH-CAH-TOA
Review SOH-CAH-TOA, solve a few right triangles, and write down which ratio still feels shaky.
Build a unit-circle chart for 0
Build a unit-circle chart for 0, 30, 45, 60, and 90 degrees, then mirror the signs into each quadrant.
Practice identities and equations
Practice identities and equations, but require one sentence explaining each algebra move.
Graph sine
Graph sine, cosine, and tangent; label period, amplitude, shifts, and asymptotes directly on the graph.
Finish with law of sines
Finish with law of sines, law of cosines, and a mixed set so the skills do not stay in separate boxes.
Questions students usually ask
What should I learn first in trigonometry?
Start with right-triangle ratios and the unit circle. Those two ideas quietly power most trig values, equations, and graphs later.
Do I need to memorize every formula?
Memorize the core identities, but do not stop there. Say what each formula does and practice recognizing when it helps.
How do I get better at trig graphs?
Start from the parent graph, mark one full period, then apply amplitude, period, phase shift, and vertical shift in that order.
Keep the next study session focused.
Choose one check-in, open the matching lesson, and write down the smallest skill that still feels shaky. That is the next win.
Right-Triangle Trig Check-In
Try each question first. Then open the answer and notice the small move that makes the problem work.
Show answer
Use sine because sine compares opposite to hypotenuse. So sin(theta)=9/15=3/5.
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Tangent means opposite divided by adjacent. You can picture 12 parts opposite and 5 parts adjacent from the angle.
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Cosine. A good tutor trick is to say CAH from SOH-CAH-TOA: cos(theta)=adjacent/hypotenuse.
Unit Circle Check-In
Try each question first. Then open the answer and notice the small move that makes the problem work.
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1/2. On the unit circle, sine is the y-coordinate, and the 30-degree point has y=1/2.
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1/2. Cosine is the x-coordinate, and the 60-degree point has x=1/2.
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Negative. Cosine follows the x-coordinate, and x-values are negative in Quadrant II.
Identity Check-In
Try each question first. Then open the answer and notice the small move that makes the problem work.
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cos^2(theta). Start with sin^2(theta)+cos^2(theta)=1, then subtract sin^2(theta) from both sides.
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tan(theta)=sin(theta)/cos(theta). This is often the easiest rewrite when an expression has too many trig functions.
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sec(theta)=1/cos(theta). If you forget secant, connect it to cosine first.
Trig Equations Check-In
Try each question first. Then open the answer and notice the small move that makes the problem work.
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theta=30 degrees and 150 degrees. Sine is positive in Quadrants I and II.
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Trig functions repeat, and the same output can happen at more than one angle. That is why the interval matters.
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Isolate cosine first: 2cos(theta)=1, so cos(theta)=1/2. Then use the unit circle.
Graphing Check-In
Try each question first. Then open the answer and notice the small move that makes the problem work.
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3. The number in front stretches the sine wave vertically, so the graph rises 3 units above and below the midline.
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The period becomes pi instead of 2pi. The 2 makes the graph complete a full cycle twice as fast.
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Tangent, secant, cosecant, and cotangent can have vertical asymptotes. Mark those asymptotes before sketching the curve.
Applications Check-In
Try each question first. Then open the answer and notice the small move that makes the problem work.
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When you have a non-right triangle with a side-angle opposite pair. That pair gives the proportion something to hold onto.
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Area = (1/2)ab sin(C). The angle C must sit between the two known sides a and b.
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s = r theta. Check that theta is in radians before using the formula.