Can I scan a trig problem from a photo?

Yes. Click the green Scan button next to the expression input, upload a photo or PDF of your homework, and our AI extracts every trig problem on the page along with the angle unit (degrees or radians). Pick one to fill the form and solve. Works on textbook pages, exam papers, and handwritten work.

How do I evaluate trig functions at any angle?

Enter the trig function and angle like sin(45) or cos(pi/3). For special angles (0, 30, 45, 60, 90 degrees and their multiples), you get exact values with radicals. For other angles, you get decimal approximations. Toggle between degrees and radians using the unit button.

How do I find the quadrant of an angle?

Switch to Quadrant mode and enter any angle. The calculator normalizes it to 0-360 degrees, tells you the quadrant (Q1-Q4), shows the reference angle, and displays the signs of all 6 trig functions using the ASTC rule (All Students Take Calculus).

What are coterminal angles?

Coterminal angles share the same terminal side on the unit circle. They differ by multiples of 360 degrees (or 2 pi radians). For example 30, 390, and -330 degrees are all coterminal. Our calculator shows 3 positive and 3 negative coterminal angles for any input.

What are the exact values of trig functions for special angles?

Special angles (0, 30, 45, 60, 90 degrees) have exact trig values using fractions and square roots. For example sin(30)=1/2, cos(45)=sqrt(2)/2, tan(60)=sqrt(3). This calculator shows all 6 function values for every special angle.

What is the ASTC rule for trigonometry?

ASTC stands for All Students Take Calculus. It tells which trig functions are positive in each quadrant: Q1 All positive, Q2 Sine positive, Q3 Tangent positive, Q4 Cosine positive. The reciprocal functions follow: csc with sin, sec with cos, cot with tan.

How do I convert between degrees and radians?

To convert degrees to radians multiply by pi/180. To convert radians to degrees multiply by 180/pi. For example 90 degrees = pi/2 radians and pi/3 radians = 60 degrees. Our calculator accepts both units with a single toggle.

Trigonometric Function Calculator

Type sin, cos, tan, pi naturally — use the Visual editor for fractions and roots. Evaluate: sin(45), cos(pi/3) · Quadrant / Coterminal: just an angle like 210 or 750.

Angle unit

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sin θ

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Type a trig expression above and hit Evaluate.

Calculate to see the unit circle / graph.

Understanding Trigonometric Functions

The six trigonometric functions — sine, cosine, tangent, cosecant, secant, and cotangent — relate angles to ratios of sides in a right triangle. On the unit circle (radius 1, centred at the origin), for any angle θ the coordinates of the terminal point are (cos θ, sin θ). These functions are foundational in physics, engineering, signal processing, and navigation.

Primary Functions

sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent

Reciprocal Functions

csc θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ

Key Relationships

sin²θ + cos²θ = 1
tan θ = sin θ / cos θ
Period: sin, cos = 2π; tan = π

Special Angle Values

The angles 0°, 30°, 45°, 60°, 90° produce exact trig values using fractions and square roots. Memorising this table is essential for precalculus, calculus, and standardised tests.

Angle	sin	cos	tan	csc	sec	cot
0°	0	1	0	undef	1	undef
30°	1/2	√3/2	1/√3	2	2/√3	√3
45°	√2/2	√2/2	1	√2	√2	1
60°	√3/2	1/2	√3	2/√3	2	1/√3
90°	1	0	undef	1	undef	0

Memory trick: sin values for 0°, 30°, 45°, 60°, 90° follow √0/2, √1/2, √2/2, √3/2, √4/2. Cosine is the same sequence reversed.

ASTC Rule — Signs by Quadrant

The mnemonic “All Students Take Calculus” tells which trig functions are positive in each quadrant: Q1 All · Q2 Sine · Q3 Tangent · Q4 Cosine.

Example: Evaluate sin(150°)
1. 150° is in Q2 → reference angle = 180° − 150° = 30°
2. sin(30°) = 1/2
3. In Q2 sine is positive (ASTC: S)
4. sin(150°) = +1/2 ✓

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